Specs Kyogre: Too slow for our fishy friend. After SR damage or a couple layers of spikes, the OHKO is guaranteed long before his Thunder wipes you out. The free rain is nice.
Scarf Kyogre: The fastest variants can speed tie, but most of these will simply be OHKO'd regardless of hazards.
Other Kyogre: The bulkiest can only be 2HKO'd, so make sure to weaken them a bit first. Even max HP/Def Kyogre takes 60-70% from Head Smash.
Arceus(Resistant to Rock): will only be 3HKO'd by Head Smash.
Arceus(Fighting): Zen Headbutt will actually 2HKO after Stealth Rock, which means that you can revenge kill a weakened one fairly easily, or you can headbutt a fresh one while they set up and then finish them off before they can kill you. (ExtremeSpeed can only 12HKO from a non-STAB Arceus.)
Arceus(Steel): Earthquake gets a 2HKO on this guy. His strongest attack against Relicanth is Thunder. This attack can do up to 99% damage to Relicanth, but it cannot OHKO.
Arceus(Ground): Ground-type Judgement will OHKO Relicanth flat out. But before it does that, Aqua Tail will deal 75-85% damage. If they're weakened and you have the freedom to select that move, they're a non-entity.
Arceus(Weak to Rock):
All standard sets are OHKO'd by Head Smash before they can move. The only downside is that they tend to have a lot of health. Taking one down from full health will remove 190 of Relicanth's 342 HP, so be cautious of that.
Arceus(Others):
Every one of these is 2HKO'd after stealth rock, with less bulky variants not requiring hazards. Of particular note is Extreme Killer Arceus, which can only touch you with the slow Earthquake. Relicanth can take 5 unboosted ExtremeSpeeds before falling, or 3 after a Swords Dance. Of course, basically all forms carry either Earthquake or Brick Break, both of which can murder Relicanth. As a revenge killer, Relicanth does swell. Be sure that the target Arceus is at least under 80% HP for maximum KO potential.
Blaziken: All standard sets are OHKO'd by Head Smash (usually) or Aqua Tail (always) before they can move. Even after a speed boost.
Cloyster: Head Smash will almost kill this guy twice. Beware his maximum speed sets after a Shell Smash, as its Hydro Pump has a decent chance to OHKO Relicanth in the rain. His physical moves can be tanked with ease.
Cresselia: All standard sets are 2HKO'd. She can't even touch Relicanth without Hidden Power Fighting, which is an occasional 2HKO. (But she'll never get off two.)
Darkrai: All standard sets are OHKO'd by Head Smash before they can move.
Deoxys: All standard sets are OHKO'd by Head Smash before they can move.
Deoxys-A: All standard sets are OHKO'd by Head Smash before they can move.
Deoxys-D: Many forms are OHKO'd by Head Smash after stealth rock. The bulkier sets will be 2HKO'd. Its low health means that you won't even take much recoil!
Deoxys-S: OHKO'd by Head Smash, but beware. While Super Power will only get a 2HKO on Relicanth at best, a select few carry Energy Ball or Grass Knot to slaughter Kyogre and his buddies. Grass Knot you can take on the nose, if Relicanth is healthy enough. Energy Ball has a chance to OHKO even without entry hazard damage on Relicanth. If you expect they have a grass move, be very cautious. Otherwise, even the best Superpower available will only deal ~50% damage, and few Deoxys-S are maximally invested in Attack. Smash these ones. If Relicanth is damaged, it may be best to run away. This is one of the few Pokemon that will outrun you without boosts.
Dialga: All sets are easily 2HKO'd by Earthquake. Easy 3HKO if you're locked into Head Smash already.
Ditto: If you end up fighting yourself, don't panic. Hit them with Head Smash. They can't quite OHKO you, and you can't quite OHKO them. The last thing you want to do is let them get off a free Head Smash on a switch. Do what you can, then let something of yours revenge kill.
Dugtrio: All standard sets are OHKO'd by any of 6 separate recommended attacks before they can move.
Excadrill: Assuming you encounter it under the rain, you can OHKO before they move with either Earthquake or Aqua Tail. (Aqua Tail deals quite a bit more, but either is overkill.) Head Smash is not recommended, since it is only a 3-4HKO.
Ferrothorn: A hard counter to Relicanth. Best you can do is 3HKO with Head Smash. Sufficient hazards can reduce this to a 2HKO, but you're going to get Power Whipped long before this happens.
Forretress: Easy 2HKO, and it can't do much to stop you. Volt Switch can only 4HKO Relicanth.
Froslass: All standard sets are OHKO'd thrice over by Head Smash before they can move.
Garchomp: 2HKO with Head Smash, but more damage can be done with Aqua Tail. Decent chance to OHKO with Aqua Tail after Stealth Rock.
Gastrodon: Guaranteed 2HKO with Head Smash. Earth Power can hurt, but usually won't kill you outright.
Genesect: Most forms are automatically OHKO'd before they can move by Head Smash. 252 HP/Def is unlikely on a Genesect, but it allows it a large chance for survival. Max SpA Genesect will only 2HKO Relicanth with Thunderbolt. Thunder, while rare, is enough to kill Relicanth immediately. The recoil after taking the electric hit will usually finish you off, so be wary.
Giratina: Physically defensive sets can be 2HKO'd after stealth rock damage. Specially defensive sets need no hazards.
Giratina-O: All common sets are 2HKO'd. Only max defense Giratina requires hazard damage.
Gliscor: Even the bulky Substitute sets used in Ubers is OHKO'd by Aqua Tail and very easily 2HKO'd by Head Smash. The 75-85% damage is enough to prevent them from setting up a Substitute, and you can smash again. It can return fire with Earthquake for ~50% damage.
Gorebyss: All standard sets are OHKO'd by Head Smash before they can move. Fun fact: Relicanth is still faster than Hydration Gorebyss under the rain after a Shell Smash. Go nuts. If they've Smashed and have Swift Swim, beware the Hydro Pump!
Groudon: If it's sunny out, DO NOT ENGAGE. If it's raining somehow, go to town with your water moves. Only extraordinarily bulky Groudon can withstand an Aqua Tail or Waterfall. With SR out, Aqua Tail even has a small chance to OHKO. In any weather except Rain, Groudon's Earthquake will simply slaughter Relicanth.
Heatran: All standard sets are OHKO'd by Aqua Tail before they can move. Head Smash will always OHKO after stealth rock damage. Relicanth fears neither of Heatran's STABs and will only take significant damage from HP grass. (Or Solarbeam if it's sunny, but Relicanth shouldn't be used outside of rain.)
Heracross: All standard sets are OHKO'd by Head Smash, Aqua Tail, or Zen Headbutt before they can move.
Ho-Oh: All standard sets are OHKO'd by Head Smash or Aqua Tail before they can move.
Hydreigon: All standard sets are OHKO'd by Head Smash before they can move.
Jirachi: Bulky forms will only be 2HKO'd by Aqua Tail. Frailer forms can be OHKO'd after Stealth Rock. Earthquake will deal an almost negligibly lower amount of damage.
Jynx: All standard sets are OHKO'd four or five times over by Head Smash before they can move.
Kabutops: Swift Swim Kabutops will outspeed Relicanth, but you can OHKO it with your choice of Head Smash, Aqua tail, or Earthquake. The most you can take is ~75% from Waterfall. It would be thus recommended to use Aqua Tail or Earthquake to avoid killing yourself.
Kingdra: All standard sets are OHKO'd by Head Smash, but Swift Swim allows Kingdra to OHKO first with Hydro Pump or Draco Meteor. Still, a poor switch by the enemy can be catastrophic.
Kyurem-W: All standard sets are OHKO'd by Head Smash before they can move.
Kyurem-B: All standard sets are OHKO'd by Head Smash before they can move.
Landorus: All standard sets are OHKO'd by Aqua Tail (through screens, even!) or Head Smash (less powerful) before they can move.
Landorus-T: Aqua Tail will utterly wreck all but the bulky pivot set. (Which takes 86-102% damage from it.) If they're foolish enough to switch in a Landorus-T to fight you, either Stealth Rock damage will be enough to make it a guaranteed OHKO or you can just hit them again for the 2HKO.
Latias: All standard sets have a decent chance to be OHKO'd by Head Smash before they can move. Stealth rock seals the deal.
Latios: All standard sets are OHKO'd by Head Smash before they can move.
Lucario: All standard sets are OHKO'd by Earthquake or Aqua Tail before they can move.
Ludicolo: All standard sets are OHKO'd by Head Smash before they can move.
Lugia: Standard Calm Mind are OHKO'd by Head Smash before they can move. The Great Wall set has a large chance to be OHKO'd, which is guaranteed after Stealth Rock.
Magnezone: All standard sets are OHKO'd by Earthquake before they can move. Aqua Tail is a solid 2HKO (chance to OHKO after spikes), if you fear they're baiting you into Earthquake against a flying or levitating foe.
Mamoswine: All standard sets are OHKO'd by Aqua Tail or Head Smash before they can move. Mamoswine at +1 speed can only be outrun by a Jolly Relicanth, who will only be able to guarantee the OHKO without spikes with Aqua Tail.
Manaphy: Decent chance to OHKO with Head Smash after Stealth Rock damage, otherwise 2HKO on the Calm Mind set. The Tail Glow set takes a tad more damage, enough to guarantee the OHKO with stealth rocks or have a 50% shot without.
Metagross: Best you can do is 2HKO with Aqua Tail or Earthquake. Hammer Arm can mess you up if Relicanth is wounded.
Mew: Good chance to OHKO with hazards down, otherwise just a solid 85-95% average damage to most sets.
Mewtwo: Guaranteed OHKO with Head Smash and Stealth Rock, otherwise you come very close. All life orb sets are guaranteed OHKOs after one round of attacking. (Which means Relicanth can revenge kill him easily, being faster than every nonscarfed form.)
Omastar: You'll speed tie this one, depending on your choice of nature. Good shot to OHKO with Head Smash. Earthquake can do so after SR damage. Beware both Hydro Pump and Earth Power, as Relicanth is no special tank.
Palkia: All standard sets are OHKO'd by Head Smash before they can move. Strange physically bulky sets will require Stealth Rock damage.
Qwilfish: Faster than Relicanth. All standard sets are OHKO'd by Head Smash, Earthquake, and Zen Headbutt. Luckily it's a physical sweeper, and none of its common moves will deal more than 50% damage to Relicanth. Beware Thunder Wave.
Raikou: All standard sets are OHKO'd by Head Smash, Aqua Tail, and Earthquake before they can move.
Rayquaza: All standard sets are OHKO'd by Head Smash. Usually twice over, just in case you were wondering about killing Rayquaza through Reflect. Rayquaza
does have a 50% chance to OHKO Relicanth with Earthquake due to that sky-high attack stat. Outrage will never OHKO a Relicanth at full health. Play your cards right, and you can beat Sky Dragon with Old Fish.
Reshiram: All standard sets are OHKO'd by Head Smash before they can move. Earthquake and Aqua Tail will also OHKO, but are only guaranteed after at least 6% damage from entry hazards.
Salamence: All standard sets are OHKO'd by Head Smash before they can move.
Scizor: All standard sets have a moderate chance to be OHKO'd by Head Smash before they can move. Stealth Rock guarantees it, and grants Aqua Tail a 100% chance to OHKO instead of 6.25%.
Shaymin-S: Terrified of grass-types as Relicanth normally is, this one flies. So it's dead. All standard sets are OHKO'd by Head Smash before they can move. Aqua Tail is a solid 2HKO, but you
really want it dead before it uses Seed Flare.
Shedinja: All sets are murdered up to two thousand times over by Head Smash before they can move. Astounding.
Shiftry: All standard sets are OHKO'd by Head Smash before they can move. Do not engage under sunlight.
Skarmory: Head Smash is a solid 2HKO, but Aqua Tail does only slightly less. If Skarmory tries to Roost, Aqua Tail is by far superior. If it's not raining and Skarmory roosts, Earthquake does just as much as Aqua Tail does under rain. (But then they can stop roosting and wall you forever.)
Smeargle: All standard sets are OHKO'd by a plethora of moves before they can move. You can fuck this guy up six ways to Tuesday. The FEAR version might stop you, but no more than it would stop any of your other Pokemon.
Tentacruel: All standard sets are OHKO'd by Head Smash or Earthquake before they can move. Zen Headbutt is another option to OHKO, but is only guaranteed after hazards.
Terrakion: All standard sets are OHKO'd by Aqua Tail or Earthquake before they can move. Earthquake requires hazards to guarantee. Zen Headbutt can deal heavy damage, but won't commonly OHKO without at least 15% damage from hazards. Relicanth even outruns Scarf Terrakion under the rain.
Thundurus: All standard sets are OHKO'd by Head Smash and Aqua Tail. Prankster sets can paralyze Relicanth and leave him wide open for Evisceration By Lightning, though, so play it safe.
Thundurus-T: All standard sets are OHKO'd by Head Smash and Aqua Tail.
Tornadus: All standard sets are OHKO'd by Head Smash and Aqua Tail. As with Thundurus, beware Prankster.
Tyranitar: Most standard sets are OHKO'd by Aqua Tail. A OHKO with Head Smash is possible after at least 15% hazard damage. ScarfTar only needs a single layer of spikes to be OHKO'd by Head Smash as well.
Venusaur: Only extraordinarily bulky Venusaur will avoid the instant OHKO from Relicanth. As with most sun sweepers, don't face it head on in the sun. Grass moves are anathema to the amaranth coelacanth.
Victini: Head Smash and Aqua Tail will both eviscerate Victini before it can move. Earthquake will deal massive damage, but only OHKO after some hazard damage. Fun fact: Relicanth can take as little as 7% damage from Scarf Victini's V-Create, the only set faster than Relicanth. Bolt Strike, on the other hand, will cleanly 2HKO. Don't let Victini attack twice.
Whimsicott: Beware Prankster. Otherwise, you can outspeed it and OHKO with Head Smash. If all it's doing with Prankster is Taunt and Encore, well, you can give it what it asks for.
Wobbuffet: Oh shit. Wobbuffet tends to eat Choice sweepers for breakfast. The worst part is that your maximum damage is only ~78% with Head Smash. It's possible with enough hazards, but most likely you're going to get countered pretty hardcore.
Xatu: All standard sets are OHKO'd by Head Smash.
Zekrom: Frailer sets can be OHKO'd by Head Smash after hazard damage, otherwise you'll only 2HKO. 21% hazard damage can guarantee a OHKO on middling bulk sets, and will give a small chance to OHKO on even the bulkiest Zekrom. If you're going to fight Zekrom with Relicanth, be sure to kill it in one hit. Bolt Strike will do terrible things.
Zoroark: All standard sets are OHKO'd by Head Smash and Aqua Tail.