Here is the full list of all 13 Inexistence Rebirth achievements.
Getting to Claos Castle
kill 100 monsters
Defeating a boss
Find the 10 hidden puzzle pieces
Obtain all equipment
Discover 100% of the maps
Open all chests
Get all the skills
Reach level 25
Finish the game
Finish the game in hard mode
Finish the game in "Sister" mode
Complete the bestiary