The purple Giant Mewtwo represents the Devil, a humanoid antagonist with an elongated tail and a dark color scheme who grows to giant size during his boss battle.
The stage represents "One Hell Of A Time", a volcanic-filled stage which features the final boss battle against the giant-sized Devil in Cuphead.
The music track, without DLC, features a jazz style, referencing the jazz-inspired soundtrack of Cuphead.
The Bomberman Assist Trophy enemy references the bat-winged bombs that the Devil summons, which can explode into a huge radius if not destroyed.
Mewtwo starting off with a Death's Scythe references the pitchfork that the Devil carries around in Cuphead.
Other trivia:
This spirit's Neutral type references the Devil's dark color scheme.
This spirit's Energy Shot Attack/Resistance ↑ ability references the Devil's usage of energy attacks during the first phase of his boss battle.