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