Here is the full list of all 43 Rainbow Skies trophies - there are 26 bronze, 13 silver, 3 gold and 1 platinum.
Unlock all other trophies.
Steal at least 100 items from monsters.
Discover 30 different fish.
Complete 75% of the item encyclopedia.
Catch at least 75 fish.
Unearth at least 50 buried treasures.
Win 100 prizes of category B or better.
Increase the progress of all main quests from 90% to 100%.
Cause 100,000 damage with any attack.
Increase the progress of all main quests from 80% to 90%.
Improve equipment 100 times at the Blacksmith using any materials.
Bring all three main characters to level 70 or higher.
Complete 50 or more optional side quests. Repeatable quests only count once!
Increase the progress of all main quests from 70% to 80%.
Increase the progress of all main quests from 60% to 70%.
Purchase 100,000 coins worth of items from any merchant.
Expand a skill pattern of any skill 30 times.
Survive 100 game days in the world of Lunah. (Defeats are permitted.)
Use and study 40 magic books.
Increase the progress of all main quests from 50% to 60%.
Find a total of 25 Moon Trophies.
Increase the progress of all main quests from 40% to 50%.
Completely explore 40 areas. (100%)
Discover and explore at least 20 optional areas or dungeons.
Upgrade any piece of equipment to '+5' by using crystals.
Unlock a five star battle rank at the Tutor.
Increase the progress of all main quests from 30% to 40%.
Play at least 200 hours (game world time, not Earth time!) with an active light spell. It doesn't matter if the light is activated using items or magic.
Defeat 1,000 or more monsters.
Achieve 75 amount of level ups. This includes all team members, monsters and main characters alike.
Find and collect at least 150 items that can be picked or collected in the world.
Achieve sales level 2 in any shop.
Inflict negative conditions on enemy monsters at least 100 times.
Increase the progress of all main quests from 20% to 30%.
Eat 50 of any food to do more damage in battle.
Hatch 5 monster eggs.
Spend at least 500 Rainbow Coins at the Healer.
Raise the level of any skill to 25 or higher.
Increase the progress of all main quests from 10% to 20%.
Upgrade weapons or equipment by using them in battle 15 times.
Permanently increase any attribute for any characters 10 times using food.
Complete 10% of all quests in the main story.
Defeat all of the monsters from the quest 'Monsters Everywhere.'