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