Chansey
252 SpA Life Orb Mewtwo-Mega-Y Psycho Boost vs. 252 HP / 252 SpD Eviolite Chansey: 207-243 (29.4 - 34.5%) -- 6% chance to 3HKO
This looks like it's fine, right? Until...
252 SpA Life Orb Mewtwo-Mega-Y Secret Sword vs. 252 HP / 252+ Def Eviolite Chansey: 434-512 (61.6 - 72.7%) -- guaranteed 2HKO
252 Atk Life Orb Mewtwo-Mega-Y V-create vs. 252 HP / 252+ Def Eviolite Chansey: 376-442 (53.4 - 62.7%) -- guaranteed 2HKO
These are both fairly common moves on Contrary Mega Mewtwo Y - While you wall the 2 main moves that this set "needs", you lose to 2 common coverage options. This is also ignoring how the 4th move's two first options, Taunt and Encore, also give Unaware a hard time, because it means you can lock them into Metal Burst and chip them into Sword range after they switch in, or it means you can lock them into recovery and eventually beat them with one of the two common coverage options mentioned.
Unaware Chansey answers Mega Mewtwo Y sets that are using Overheat, Moongeist Beam or Earth Power in the 3rd slot while also running Strength Sap and King's Shield in the fourth slot - But really, how good are those Contrary Mega Mewtwo Y sets? This is also ignoring how easy it is to passively chip Unaware Chansey, or just Pursuit it - Without Fur Coat, it's not too bulky.
Giratina
I don't even need to calc, it gets 2HKOed by Fleur on the switchin and loses to Moongeist.
Kyogre-Primal
While this one is one of the best Contrary answers on paper, it can't switch in on Mega Mewtwo Y's Psycho Boost if Stealth Rock is up, if it's taken equivalent chip (pretty easy to get) or if Mega Mewtwo Y is running Life Orb.
252 SpA Mewtwo-Mega-Y Psycho Boost vs. 252 HP / 252+ SpD Kyogre-Primal: 160-189 (39.6 - 46.7%) -- 33.2% chance to 2HKO after Stealth Rock
252 SpA Life Orb Mewtwo-Mega-Y Psycho Boost vs. 252 HP / 252+ SpD Kyogre-Primal: 208-246 (51.4 - 60.8%) -- guaranteed 2HKO
Registeel
252 Atk Life Orb Mewtwo-Mega-Y V-create vs. 252 HP / 252 Def Registeel: 338-398 (92.8 - 109.3%) -- 56.3% chance to OHKO after Leftovers recovery
Loses to Life Orb if it switches in on literally anything else, loses to Taunt + Secret Sword or Encore + Secret Sword on non-Life Orb variants.
252 SpA Life Orb Mewtwo-Mega-Y Secret Sword vs. 252 HP / 252 Def Registeel: 195-231 (53.5 - 63.4%) -- guaranteed 2HKO after Leftovers recovery
Zygarde-C
It's still got Giratina's Fairy weakness, so it still loses to Fleur Cannon and can't switch in very well on LO Psycho Boost.
252 SpA Life Orb Mewtwo-Mega-Y Psycho Boost vs. 252 HP / 252 SpD Zygarde-Complete: 331-390 (52 - 61.3%) -- 96.1% chance to 2HKO after Leftovers recovery
252 SpA Life Orb Mewtwo-Mega-Y Psycho Boost vs. 252 HP / 252+ SpD Zygarde-Complete: 300-355 (47.1 - 55.8%) -- 20.7% chance to 2HKO after Leftovers recovery
252 SpA Life Orb Mewtwo-Mega-Y Fleur Cannon vs. 252 HP / 252 SpD Zygarde-Complete: 411-484 (64.6 - 76.1%) -- guaranteed 2HKO
252 SpA Mewtwo-Mega-Y Fleur Cannon vs. 252 HP / 252+ SpD Zygarde-Complete: 286-338 (44.9 - 53.1%) -- 0.4% chance to 2HKO after Leftovers recovery
Dialga
252 Atk Life Orb Mewtwo-Mega-Y V-create vs. 252 HP / 252 Def Dialga: 198-233 (49 - 57.6%) -- 52.3% chance to 2HKO after Leftovers recovery
252 SpA Life Orb Mewtwo-Mega-Y Fleur Cannon vs. 252 HP / 252+ SpD Dialga: 181-213 (44.8 - 52.7%) -- 24.6% chance to 2HKO after Stealth Rock and Leftovers recovery
252 SpA Life Orb Mewtwo-Mega-Y Secret Sword vs. 252 HP / 252 Def Dialga: 229-270 (56.6 - 66.8%) -- guaranteed 2HKO after Stealth Rock and Leftovers recovery
Mega Audino
252 SpA Life Orb Mewtwo-Mega-Y Psycho Boost vs. 252 HP / 252+ SpD Audino-Mega: 247-292 (60.2 - 71.2%) -- guaranteed 2HKO after Leftovers recovery
252 SpA Mewtwo-Mega-Y Psycho Boost vs. 252 HP / 252+ SpD Audino-Mega: 190-225 (46.3 - 54.8%) -- 10.5% chance to 2HKO after Leftovers recovery
Can't switch in on the main STAB, and can't do much back because it's forced to keep recovering.
NDM and Solgaleo lose to Moongeist, Fire coverage or Ground coverage, and struggle vs Sap variants. Won't bother providing calcs.
Yveltal
252 SpA Mewtwo-Mega-Y Fleur Cannon vs. 248 HP / 252+ SpD Yveltal: 282-332 (61.9 - 72.9%) -- guaranteed 2HKO
Loses to Fleur Cannon, even without Life Orb, and...
252 Atk Life Orb Mewtwo-Mega-Y V-create vs. 248 HP / 252 Def Yveltal: 231-273 (50.7 - 60%) -- 86.7% chance to 2HKO after Leftovers recovery
Loses to this after Life Orb. Can't switch in very well.
Unaware Aegislash is garbage and loses to like Fire/Ground/Ghost move MMY. Not even gonna bother calcing.
Celesteela is one of the best Unawares for beating MMY - If MMY doesn't have Moongeist or Fire-type coverage it just wins, but it loses to MMY when it has either of the two. Also Unaware Celes is lol
Tyranitar-Mega
252 Atk Life Orb Mewtwo-Mega-Y V-create vs. 252 HP / 252 Def Tyranitar-Mega: 84-99 (20.7 - 24.5%) -- possible 6HKO after Leftovers recovery
252 SpA Life Orb Mewtwo-Mega-Y Fleur Cannon vs. 252 HP / 252+ SpD Tyranitar-Mega: 317-374 (78.4 - 92.5%) -- guaranteed 2HKO after Leftovers recovery
252 SpA Life Orb Mewtwo-Mega-Y Secret Sword vs. 252 HP / 252 Def Tyranitar-Mega: 390-463 (96.5 - 114.6%) -- 81.3% chance to OHKO after Leftovers recovery
Loses to LO Fleur Cannon and Sword, if it's not Lefties loses to V-Create on the switch as well. Can switch in on Psycho Boost but nothing else. Life Orb has a harder time dealing w megatar however.
MGyara loses to Fleur Cannon and Secret Sword on the switch, the calcs are 2HKOs from experience so I won't post em.
Cresselia
Honestly, Unaware Cresselia is probably the closest thing to a Contrary Mega Mewtwo Y answer, but it loses to Moongeist Beam sets and V-Create after Stealth Rock.
252 Atk Life Orb Mewtwo-Mega-Y V-create vs. 252 HP / 252 Def Cresselia: 198-233 (44.5 - 52.4%) -- 80.1% chance to 2HKO after Stealth Rock and Leftovers recovery
Ho-Oh
252 SpA Life Orb Mewtwo-Mega-Y Psycho Boost vs. 252 HP / 252+ SpD Ho-Oh: 214-253 (51.4 - 60.8%) -- guaranteed OHKO after Stealth Rock and Leftovers recovery
Can't switch in on Psycho Boost and it loses 50% everytime Stealth Rock is up.
Mega Sableye
252 SpA Life Orb Mewtwo-Mega-Y Fleur Cannon vs. 248 HP / 252+ SpD Sableye-Mega: 328-387 (108.2 - 127.7%) -- guaranteed OHKO
lol
Mega Steelix
252 SpA Life Orb Mewtwo-Mega-Y Psycho Boost vs. 252 HP / 252+ SpD Steelix-Mega: 149-177 (42 - 50%) -- 10.2% chance to 2HKO after Stealth Rock
Which doesn't seem bad, until...
252 Atk Life Orb Mewtwo-Mega-Y V-create vs. 252 HP / 252 Def Steelix-Mega: 239-283 (67.5 - 79.9%) -- guaranteed 2HKO after Stealth Rock
You lose on the switch, even at a minroll w/ lefties.
252 SpA Life Orb Mewtwo-Mega-Y Earth Power vs. 252 HP / 252+ SpD Steelix-Mega: 260-307 (73.4 - 86.7%) -- guaranteed 2HKO after Stealth Rock
Megalix can try to switch in on Fleur Cannon, but it still loses to the same things that beat it - Only difference is Megalix actually gets a turn to do something.
Darmanitan-Zen
252 SpA Life Orb Mewtwo-Mega-Y Earth Power vs. 252 HP / 252+ SpD Darmanitan-Z: 242-286 (58.4 - 69%) -- guaranteed 2HKO after Stealth Rock
Unaware Darmanitan Zen can't really stall out LO's recoil:
http://replay.pokemonshowdown.com/gen7balancedhackmons-875003005
It can't really switch in either - It loses eventually.
Meloetta
252 Atk Life Orb Mewtwo-Mega-Y V-create vs. 252 HP / 252+ Def Meloetta: 242-285 (59.9 - 70.5%) -- guaranteed 2HKO after Stealth Rock and Leftovers recovery
Doesn't win vs V-Create w/ Life Orb, but w/ Leftovers Meloetta beats it without Life Orb unless it gets crit.