Here is the full list of all 14 SteamWorld Dig (JP) trophies - there are 12 bronze, 1 silver and 1 gold.
You found Vectron!
You found the Old World!
Defeat a turtle submerged in water.
You found Archaea!
Immortalization of a destructible steambot.
Complete the game with more than 20000 gold collected in total.
Complete the game in less than 2 hours, 30 minutes.
Complete the game with more than 150 orbs collected in total.
Complete the game without getting killed once.
Get all four gold stars in the same playthrough.
Find all secret areas in the caves.
Maximize all upgrades.
Reach the bottom of the world.
Destroy two generators before entering Vectron.