"Collect all singleplayer skins"



You can find the skins in the following locations:

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You can equip them in the igloo at the starting area:

"Find all the Moles and restore the band"



You need to find all the moles in a specific order. Every mole you find gives you a hint for the location of the next one.
1.
2.
3.
4.
5.
6.

"Collect all the music"



There are three missing vinyl records, which can be obtained by:

1. Reaching the top
2. Finding all the moles
3. Talking to the 8-bit penguin

"Complete all time trials"



In the starting area you can find a polar bear who will let you compete in the time trials.

"Get Platinum on all time trials"



Platinum times:

Level 1: 01:10:000
Level 2: 02:00:000 (this one is bugged and should be lower if you consider the given gold time)
Level 3: 00:50:000
Level 4: 01:05:000
Level 5: 01:00:000
Level 6: 00:55:000
Level 7: 01:10:000
Level 8: 01:00:000
Level 9: 00:50:000
Level 10: 00:57:000 (the given times are also wrong here)

"Complete the game in under 30 minutes"



You can make this achievement easier by enabling the assist options.