Here is the full list of all 25 Battle Chef Brigade achievements.
Complete Story Mode
Achieve a total round score of 1000 points or more
Cure Ardea
Obtain extra points from a Judge for using any Expertise Tome 5 times
Complete all of Pontida's Jobs
Complete all of Thorn's Hunts
Complete all of Belchior's Puzzles
Use Thrash's Heavy Attack to smash a monster into 3 others
Consume 10 ingredients in one match
Join the Brigade as Mina
Deflect 10 projectiles with a heavy attack
Obtain a sample of Ambrosia
Win the practice match against Thrash
Buy 15 items
Jump on the bed 10 times
Beat the game without losing a match
Achieve 10 Daily Cook-Off victories
Reach Brigade Rank 12 in Daily Cook-Off
Stock your pantry with 30 ingredients in one match
Win a round with over 2 minutes remaining on the match clock
Win a duel without using the theme ingredient
Make a dish worth 450 points or more
Reach a combo multiplier of 10
Kill 3 enemies without touching the ground
Complete Story Mode on Hard