Overview
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Although its viability has somewhat diminished somewhat (sounds better like this imo), Dragon Arceus retains great all-round base stats and a unique mono-Dragon typing; this gives it neutrality to most other types and lets it handle to a degree an offensive behemoth in Kyogre to a degree (it seems kinda out of place waaay over there), which has notoriously few checks. For what it is worth, Dragon Arceus still remains a viable Calm Mind user and can use a Swords Dance set to good effect. Unfortunately, Fairy-types are truly its undoing, impairing its offensive potency greatly. Swords Dance Dragon Arceus has to rely on sub-optimal coverage moves if it is to overcome them, while the Calm Mind set cannot do so at all. Also, its Dragon typing ironically leaves Dragon Arceus vulnerable to other Dragon-types such as Palkia, which it can beat one-on-one but cannot switch in on, and Zekrom, a common revenge killer. Still, with proper team support, these flaws are very much surmountable, so do not let them detract from Dragon Arceus's value as a solid Arceus forme and potent offensive threat.
Calm Mind
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name: Calm Mind
move 1: Calm Mind
move 2: Judgment
move 3: Recover
move 4: Will-O-Wisp / Fire Blast
item: Draco Plate
evs: 252 HP / 80 SpD / 176 Spe
nature: Timid
Moves
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Calm Mind boosts Dragon Arceus's Special Attack and Special Defense by one stage each, which is exceedingly important if it is to pull off a late-game sweep. Judgment is the obligatory STAB move, hitting most targets for neutral damage. Recover aids Dragon Arceus in its role as a pivot, keeping it healthy and letting it switch in numerous times throughout the match. Will-O-Wisp is the preferred move in the last slot, crippling troublesome bulky Pokemon such as Steel-types that resist Dragon Arceus's STAB Judgment; in conjunction with Calm Mind and mono-Dragon typing, it can make Dragon Arceus very difficult to break with both physical and special attacks. Alternatively, Fire Blast roasts all Steel-types barring Heatran. Finally, Refresh can rid Dragon Arceus of status, letting it hold its own in Calm Mind wars with other Arceus formes using Will-O-Wisp and allowing it to set up on Pokemon like Blissey that would wall it otherwise. Note that the one major drawback to using Refresh is that it leaves Dragon Arceus completely helpless against Fairy-types.
Set Details
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With 176 Speed EVs with a Timid nature, Dragon Arceus outspeeds everything up to Timid Mega Gengar (before the latter Mega Evolves), allowing it to hit first with Judgment. 252 EVs are placed in HP and the remaining 80 EVs in Special Defense so Dragon Arceus can make the best of it's excellent natural bulk make the best of Dragon Arceus's excellent natural bulk. The Special Defense investment lets it better stomach Kyogre's and Palkia's attacks. Alternatively, a spread of 252 HP / 4 Def / 252 Spe with a Timid nature can be used with Will-O-Wisp, allowing Arceus to, at worst, Speed tie with Extreme Killer Normal Arceus and other Swords Dance Arceus formes and burn them. At any rate, it is recommended to invest fully in HP, since a main draw of using Calm Mind Dragon Arceus is that it can switch into Choice Scarf Kyogre's Water Spout at full power and avoid a 2HKO, and maximum HP EVs lets it avoid the 2HKO from this (kinda redundant, but this is an optional change).
Usage Tips
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Capitalize on Pokemon Dragon Arceus can handle by switching it in on them throughout the game. Spread burns with Will-O-Wisp and stay keep it (It sounds like you're referring to arceus as "you", which you aren't suppose to do.) healthy until a window of opportunity opens for it to switch in safely to set up late-game, such as a predicted Surf from Choice Scarf Kyogre. Even a full-powered Water Spout from Modest Choice Scarf Kyogre does a maximum of 48% damage to Dragon Arceus with the listed EV spread, so do take note of that. In general though, be prudent with the usage of Calm Mind early-game. O, and only attempt to sweep after opposing Fairy-types are removed. If you predict a Xerneas or Fairy Arceus switching in, do not hesitate to double switch to a relevant teammate. Lastly, be mindful of status. Unless it is using Refresh, Dragon Arceus is crippled by status of any sort. Burn and poison limit its longevity, and paralysis destroys its Speed advantage over many Pokemon.
Team Options
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Mega Gengar support is strongly advocated to remove Fairy-types that are immune to Dragon Arceus's Judgment. Ho-Oh can capitalize on the many common Steel-type switch-ins to Dragon Arceus to fire off its powerful STAB moves or set up a Substitute. A physically defensive variant can also help against opposing Ho-Oh, which Dragon Arceus has difficulty taking down. Additionally, a reliable Stealth Rock setter like Landorus-T goes a long way in keeping Ho-Oh in check. Defog support is recommended; Scizor is a solid candidate that fares well against Fairy-types. Xerneas and Sylveon are good teammates that can rid Dragon Arceus of status ailments; their Fairy-typing is also useful for shielding it from opposing Dragon-type moves. Most importantly, it is necessary to have teammates that can subdue a boosted and healthy Geomancy Xerneas, which can switch in and setup on Dragon Arceus with impunity easily (it's a blacklisted term lmao). Specially defensive Kyogre can take any boosted hit and phaze Xerneas with Roar, as can Multiscale Lugia with Whirlwind. Aegislash and Bronzong can handle Xerneas with Gyro Ball, although they both require Attack investment to dispatch it outright.
Swords Dance
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name: Swords Dance
move 1: Swords Dance
move 2: Outrage
move 3: Overheat
move 4: Earthquake / Iron Tail / Extreme Speed
item: Draco Plate
evs: 252 Atk / 4 SpA / 252 Spe
nature: Jolly
Moves
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Swords Dance doubles Dragon Arceus's aAttack, making it an extremely threatening sweeper with a single turn of setup. Effectively a 144 Base Power STAB move, Outrage is the star of the show; at +2 Attack, it ruins anything that doesn't resist it. For example, physically defensive Yveltal has a 81% chance of getting OHKOed after it has taken Stealth Rock damage. This is the main reason for using Swords Dance Dragon Arceus over another Swords Dance Arceus forme such as Life Orb Extreme Killer Arceus. Overheat complements Dragon Arceus's STAB Outrage excellently, burning to cinders bulky Steel-types such as Ferrothorn, Scizor, and Skarmory to cinders, all of which can stomach Outrage decently. Fire Blast can also be used here, as Overheat's Special Attack drop can be exploited with clever scouting. Earthquake is useful for hitting Klefki and Aegislash, problematic Pokemon that Dragon Arceus cannot really overcome otherwise; it also hits Heatran and Jirachi. Iron Tail is Dragon Arceus's best means of getting past Fairy-types. Although it has shaky accuracy, a +2 Attack Iron Tail has a 94% chance of OHKOing standard (108 HP / 28 Def) Geomancy Xerneas and maims most other Fairies with the exception of Klefki, which takes a minimum of 70% from the move. Extreme Speed can be used to pick off weakened Choice Scarf users that attempt to revenge kill Dragon Arceus; it also kills OHKOs Deoxys-A outright and does hefty damage to frail offensive powerhouses like Mega Blaziken, Mega Mewtwo Y, and Darkrai. Iron Head is a weaker, albeit more accurate alternative to Iron Tail, when one cannot afford to miss against Fairy-types like Geomancy Xerneas.
Set Details
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252 Spe EVs with a Jolly nature allow Dragon Arceus to outspeed everything relevant and Speed tie with other Arceus at worst. This is very important for this set as Will-O-Wisp burns from opposing support Arceus are especially debilitating. 252 Atk EVs let Dragon Arceus hit as hard as possible.
Usage Tips
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Be aware of what Dragon Arceus can and cannot KO with Outrage. +2 Outrage has a much higher chance of OHKOing many threats such as physically defensive Yveltal, Lugia, and type-neutral 252 HP support Arceus formes with Stealth Rock support, so ensure your entry hazards stay up. Being easily crippled by burns and possessing no recovery move, Dragon Arceus is very much a late-game sweeper, not to mention that Fairy-types are immune to its otherwise spammable STAB Outrage. As such, do not attempt to set up early game until its checks have been worn down or removed. However, if the opponent's team does not have a Fairy-type (or if Dragon Arceus carries Iron Tail), pulling off a quick Swords Dance to wallbreak mid-game might prove worthwhile, although this is ultimately dependent on the opposing team's team structure.
Team Options
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Once again, Mega Gengar is an excellent teammate as it can remove problematic Fairy-types that deter Dragon Arceus from sweeping. Entry hazards support is highly recommended as they allow Dragon Arceus to obtain crucial OHKOs as mentioned. Consider using suicide leads such as Deoxys-A or Deoxys-S to set up hazards rapidly on offensively inclined teams, although depending on team structure, other Stealth Rock setters such as Dialga, Groudon, and Landorus-T are perfectly viable options. In particular, if Iron Tail is not used, it is advised to have a check to boosted Geomancy Xerneas, although in this case, it cannot set up on Dragon Arceus for free, taking 50-59% from a +2 Earthquake. Scizor and Mega Lucario can both pick off weakened Xerneas with Bullet Punch. Finally, it is worth highlighting that Dragon Arceus functions brilliantly with Sticky Web support, which allows it to plow through potential revenge killers such as Mewtwo, Deoxys-A, and Choice Scarf users and lets it have an easier time setting up.
Other Options
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Dragon Arceus has few other options. Thunder can be used on the Calm Mind set to hit Kyogre, Yveltal, Ho-Oh, and Lugia harder, but note that it is only about 25% more powerful than STAB Draco Plate Judgment. (maybe something about it's accuracy too. my two cents)
Checks & Counters
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**Fairy-types**: Far and away the biggest threat to Dragon Arceus, Fairy-types are immune to its STAB moves. Geomancy Xerneas is the most notable of these, being able to freely switch in and set up on the Calm Mind set. Fairy Arceus is also very threatening, while clerics like Aromatherapy Xerneas,(AC) and Heal Bell Sylveon,(AC) or and Clefable completely wall the Calm Mind set. Whimsicott deserves mention as the Calm Mind set is completely helpless against it if not using Fire Blast. Note that all these Pokemon fall to a Swords Dance-boosted Iron Tail if it is used, so watch out for that if it has been determined that Dragon Arceus is the Swords Dance variant.
**Revenge Killers**: Choice Scarf Zekrom is the most prominent of these, outspeeding and OHKOing Dragon Arceus with Outrage.
**Blissey**: Blissey counters Calm Mind Dragon Arceus thanks to its enormous special bulk and access to Toxic.
**Ho-Oh**: Ho-Oh takes Judgment comfortably and threatens Calm Mind Dragon Arceus with its powerful dual STAB moves. The Swords Dance set KOs it with a boosted Outrage, but cannot safely set up on it predominantly due to the threat of a Sacred Fire burn.
**Lugia**: With Toxic and Whirlwind, Lugia beats any Calm Mind set lacking Refresh, and with Multiscale active, it can live any hit from the Swords Dance set and phaze it out. Even with Multiscale broken, Lugia takes a maximum of only 80% from +2 Outrage.
**Steel-types**: Bronzong can use Toxic and its favorable typing to wear down both of Dragon Arceus's sets; Overheat does a maximum of 59% to it. Heatran walls the Calm Mind set and wears it down with Toxic, and can also live any hit from the Swords Dance set barring Earthquake and phaze Dragon Arceus with Roar. Note that since Earthquake is a recommended move on the Swords Dance set, Heatran is only a shaky check to it. Skarmory takes on any Swords Dance set lacking Overheat; Ferrothorn takes hefty damage from a +2 Earthquake but can then annoy Dragon Arceus hugely with Leech Seed and Protect. Klefki can live any boosted hit that isn't Earthquake while getting in a Prankster Thunder Wave beforehand.
**Status Conditions**: Dragon Arceus loathes status of any sort; paralysis cripples all its sets, and burn or poison greatly limits its longevity, deterring it from setting up or staying on the field to sweep.