Probably Blissey for all sets, but Clodsire, Iron Treads, and Tera Fire Double Dance Koraidon can check and/or counter specific sets. Blissey and Clodsire are top two though, since Treads and Korai lack recovery.
Clodsire can counter all sets except Calm Mind if using Water Absorb, and Specs Psyshock, using Toxic and Recover stalling.
252 SpA Flutter Mane Psyshock vs. 252 HP / 192 Def Clodsire: 208-246 (44.8 - 53%) -- guaranteed 3HKO after Leftovers recovery
AV Iron Treads counters all non-Mystical Fire sets.
252 SpA Choice Specs Flutter Mane Shadow Ball vs. 252 HP / 16+ SpD Assault Vest Iron Treads: 160-190 (41.6 - 49.4%) -- guaranteed 3HKO
Tera Fire Double Dance Korai is probably the hardest to pull off, as you need a free switch. However, if you get that switch, Flame Charge OHKOs.
252 SpA Choice Specs Flutter Mane Moonblast vs. 0 HP / 0 SpD Tera Fire Koraidon: 119-141 (34.8 - 41.3%) -- 71.2% chance to 3HKO after Leftovers recovery
252 SpA Choice Specs Flutter Mane Shadow Ball vs. 0 HP / 0 SpD Tera Fire Koraidon: 202-238 (59.2 - 69.7%) -- guaranteed 2HKO after Leftovers recovery
252 Atk Orichalcum Pulse Tera Fire Koraidon Flame Charge (60 BP) vs. 0 HP / 0 Def Flutter Mane in Sun: 325-384 (129.4 - 152.9%) -- guaranteed OHKO
Blissey is the best overall solution to Mane though. You'll need to run Shadow Ball to damage it, though.
252 SpA Choice Specs Flutter Mane Psyshock vs. 4 HP / 252 Def Blissey: 266-314 (40.7 - 48.1%) -- guaranteed 3HKO
252 SpA Choice Specs Flutter Mane Moonblast vs. 4 HP / 252+ SpD Blissey: 139-165 (21.3 - 25.3%) -- 0.1% chance to 4HKO
0 SpA Blissey Shadow Ball vs. 0 HP / 4 SpD Flutter Mane: 70-84 (27.8 - 33.4%) -- 0% chance to 3HKO
Hope I helped!