Here is the full list of all 28 Princesss Peak achievements.
Get all pieces in stage 7
Get 14 pieces in stage 7
Get 7 pieces in stage 7
Get 1 piece in stage 7
Get all pieces in stage 6
Get 11 pieces in stage 6
Get 5 pieces in stage 6
Get all pieces in stage 5
Get 11 pieces in stage 5
Get 5 pieces in stage 5
Get 1 piece in stage 6
Get 1 piece in stage 5
Get all pieces in stage 4
Get 7 pieces in stage 4
Get 4 pieces in stage 4
Get 1 piece in stage 4
Get all pieces in stage 3
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Get 4 pieces in stage 3
Get 1 piece in stage 3
Get all pieces in stage 2
Get 5 pieces in stage 2
Get 3 pieces in stage 2
Get 1 piece in stage 2
Get all pieces in stage 1
Get 5 pieces in stage 1
Get 3 pieces in stage 1
Get 1 piece in stage 1