Here is the full list of all 25 Abomi Nation achievements.
Beat your first boss and gain a Mysterious Piece
Win the Abomi Racin' minigame
Recruit your first Abomi
KO 100 Abomis
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 Whack-a-Moile minigame
Win the Abomi Quiz 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 1,000 Abomis
Beat the game
Beat the game on Brutal with Permadeath on
Finish a Custom Game