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