Here is the full list of all 52 Arcane Arts Academy achievements.
Decorate Erika's room
Complete levels with 3 stars
Collect diamonds
Make a crystal potion in the laboratory
Watch all the scenes
Complete levels with at least 1 star
Complete all levels in the bookshop
Collect crowns by performing side tasks
Complete all levels in the laboratory
Find the cats
Fire up and win an already played level 5 times
Bring 20 customers to anger and leave
Complete all levels in the courtyard
Complete the tutorial
Serve sets of clothes in the courtyard
Complete all levels in the glasshouse
Grow a magic flower in the glasshouse
Serve books in a bookshop
Complete all levels in the clocktower
Expose magic lenses in the clocktower
Get "all clean" bonus on 10 levels
Serve customers with 5 hearts at the checkout
Get a bonus for full orders
Get a bonus for quick service