Here is the full list of all 14 Battle Chef Brigade Deluxe trophies - there are 11 bronze, 2 silver and 1 gold.
Beat the game without losing a duel
Complete Story Mode on Hard
Complete Story Mode
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
Join the Brigade as Mina
Win a duel without using the theme ingredient
Make a dish worth 450 points or more
Reach a combo multiplier of 10
Win a round with over 2 minutes remaining on the match clock
Kill 3 enemies without touching the ground
Win the practice match against Thrash