Here is the full list of all 25 Abomi Nation achievements.
Win the Abomi Quiz minigame
Beat your first boss and gain a Mysterious Piece
Win the Whack-a-Moile minigame
Recruit your first Abomi
Evolve an Abomi with an Evolution Crystal
Reach maximum Bond between two Abomis and make them Partners
Change an Abomi's colour using a Palette or Grayscale Orb
Win the Abomi Racin' minigame
Revive an Abomi through a code
Beat the optional Temporal Boss
Discover every area in a map
Fill the Global Abomi Archive
Spend 50,000 Shiny Pebbles across all runs
Buy something from the Temporal Store
Buy 50 things from the Temporal Store
Survive on 1HP in a Permadeath battle
Raise one stat to +6 in a Permadeath battle
Deal over 100 damage to an Abomi in one hit
KO an opponent in one hit with your Basic Attack
Use a Fire-type move while underwater
KO 100 Abomis
KO 1,000 Abomis
Beat the game
Beat the game on Brutal with Permadeath on
Finish a Custom Game