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