Here is the full list of all 11 Burning Horns: A Bara Isekai JRPG achievements.
Reach the end of the game after defeating the last enemy.
Activate the cyan color of your rainbow medallion.
Find and open all 60 chests.
Activate the red color of your rainbow medallion.
Activate the blue color of your rainbow medallion.
Find and open 40 chests.
Activate the green color of your rainbow medallion.
Activate the orange color of your rainbow medallion.
Find and open 20 chests.
Activate the yellow color of your rainbow medallion.
Activate the purple color of your rainbow medallion.