Here is the full list of all 43 Rainbow Skies trophies - there are 26 bronze, 13 silver, 3 gold and 1 platinum.
Increase the progress of all main quests from 20% to 30%.
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.
Eat 50 of any food to do more damage in battle.
Hatch 5 monster eggs.
Achieve 75 amount of level ups. This includes all team members, monsters and main characters alike.
Spend at least 500 Rainbow Coins at the Healer.
Defeat 1,000 or more monsters.
Achieve sales level 2 in any shop.
Raise the level of any skill to 25 or higher.
Inflict negative conditions on enemy monsters at least 100 times.
Increase the progress of all main quests from 10% to 20%.
Permanently increase any attribute for any characters 10 times using food.
Upgrade weapons or equipment by using them in battle 15 times.
Complete 10% of all quests in the main story.
Unlock all other trophies.
Increase the progress of all main quests from 30% to 40%.
Increase the progress of all main quests from 40% to 50%.
Increase the progress of all main quests from 50% to 60%.
Increase the progress of all main quests from 60% to 70%.
Increase the progress of all main quests from 70% to 80%.
Increase the progress of all main quests from 80% to 90%.
Increase the progress of all main quests from 90% to 100%.
Complete 75% of the item encyclopedia.
Completely explore 40 areas. (100%)
Discover and explore at least 20 optional areas or dungeons.
Find and collect at least 150 items that can be picked or collected in the world.
Complete 50 or more optional side quests. Repeatable quests only count once!
Unlock a five star battle rank at the Tutor.
Catch at least 75 fish.
Discover 30 different fish.
Win 100 prizes of category B or better.
Use and study 40 magic books.
Expand a skill pattern of any skill 30 times.
Survive 100 game days in the world of Lunah. (Defeats are permitted.)
Unearth at least 50 buried treasures.
Defeat all of the monsters from the quest 'Monsters Everywhere.'
Improve equipment 100 times at the Blacksmith using any materials.
Upgrade any piece of equipment to '+5' by using crystals.
Bring all three main characters to level 70 or higher.
Steal at least 100 items from monsters.
Cause 100,000 damage with any attack.
Find a total of 25 Moon Trophies.
Purchase 100,000 coins worth of items from any merchant.