Here is the full list of all 20 Traveler's Bastion achievements.
Win a Game in Hardcore Mode
Defeat Boss 4 in Hardcore Mode
Defeat Boss 3 in Hardcore Mode
Defeat Boss 2 in Hardcore Mode
Defeat Boss 1 in Hardcore Mode
Win a Game in Challenge Mode
Defeat Boss 4 in Challenge Mode
Defeat Boss 3 in Challenge Mode
Win in Co-op Multiplayer
Defeat Boss 2 in Challenge Mode
Complete Side Quest - Fruit Rain!
Defeat Boss 1 in Challenge Mode
Win Your First Game!
Defeat Boss 4
Defeat Boss 3
Catch Waterang 4 times in a Row
Complete Side Quest - Guardians Unite!
Defeat Boss 2
Complete Side Quest - Spell Mayhem!
Defeat Boss 1