Because of @hygge 's post, I figure it's worth posting answers for top scores (these are "the highest i've seen", not the ones in image). Spoilers below. (It is both box count and the specific secret(s) that the score used, which is enough to trivially tie the solution for a lot of the levels.)
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- Ice 1: 5 boxes; Freeze
- Ice 2: 10 boxes; Freeze,Turn
- Lilly 1: 7 boxes; Freeze
- Lilly 2: 5 boxes; All
- Move 1: 11 boxes; Turn
- Move 2: 6 boxes; All
- Size 1: 5 boxes; All
- Size 2: 5 boxes; All
- Slide 1: 6 boxes; All,Turn
- Slide 2: 9 boxes; All
- Turtle 1: 7 boxes; All
- Turtle 2: 7 boxes; All,Turn