There are 14 Trophies that can be collected.

Bronze

Burger Face
Learn how to cook a burger at Burger Face

Perfect Four
Perfect a table of four

Paperboy
Score a 92 or better on the paperboy mini-game

Pepper Chop Master
Master the Pepper Chop

Patron Pleaser
Please all 10 unique patrons

Ned Special
Purchase a special ingredient from the delivery truck and use it in each of your restaurants

Food Critic
Perfect the Food Critic at all five restaurants

All Assistants
Hire and use all assistant chefs

Mini-game Master
Beat all 5 in-kitchen mini-games

All Recipes
Unlock all recipes

All Restaurants
Five-Star all five restaurants

Silver

All Chef Spices
Purchase and use all Chef Spices appropriately

Fortified Chef
Win the Fortified Chef Battle

Gold

Coin Goal
Earn 100,000 coins

http://www.ps3trophies.com/forums/playstation-trophy-news/11211-order-up-trophy-list.html