There are 53 Trophies that can be collected.

Bronze

First Victory
Win your first battle on Rainbow Moon.

Rich?
Accumulate 2,500 Rainbow Coins in your inventory.

Crafting Novice
Improve your weapons or armor at the crafting shop for 10 times.

Pro Crafter
Improve your weapons or armor at the crafting shop for 50 times.

Side Quest Master
Complete 40 side quests or more.

Bear Up!
Accumulate 40 hours of play time.

Don't Worry, Be Happy!
Lose three battles.

Camper
Use the camp at least 25 times.

Noble Tourist
Stay overnight at the tavern 10 times.

Well Explorer
Discover and use all wells on Rainbow Moon.

Bathe in the Well
Use any recovery well at least 15 times.

Monster Farmer
Kill at least 300 of the same type of monster.

Hit and Run Fighter
Win 50 or more random encounter battles.

Scaredy Cat
Escape 30 times from a battle using the escape option.

Rainbow Pearl Collector
Accumulate 200 Rainbow Pearls with any character before spending them at the savant.

Level Fan
Reach level 100 with any of your main characters.

Silver

Half a Millionaire
Accumulate 500,000 Rainbow Coins in your inventory.

Extreme Crafter
Improve your weapons or armour at the crafting shop for 250 times.

Everlasting Perfectionist
Accumulate 100 hours of play time.

Skilled!
Acquire and learn all available skills for any of your main characters. (The skill level doesn't matter)

Level Up
Level up any of your active skills to level 50 or higher.

Level Master
Reach level 250 with any of your main characters.

Gold

Level God
Reach level 500 with any of your main characters.

Platinum

Official Rainbow Moon Hero
Obtain all other trophies to unlock the platinum trophy.

29 Secret

http://www.ps3trophies.com/forums/playstation-trophy-news/15405-rainbow-moon-trophy-list.html