Lemmings Destination/Helium. Lots of levels here that simply require all the skills, but also some that were very interesting for this challenge!
Levels that require all skills (as far as we know) are marked with an asterisk.
1 "Adventure Is Out There!" - None
2 "Attic Storage Available" - 1 climber, 2 platformers, 2 builders, 1 miner
3 "Looking Down From The Edge" - None
*4 "Lemming Rig" - 2 climbers, 1 bomber, 1 builder, 2 bashers
5 "In A Tidal Wave Of Mystery" - 2 builders, 2 miners
6 "Coffee Break In The Ballroom" - 1 climber, 1 bomber, 1 builder, 1 basher, 1 miner, 1 digger
*7 "Type B Personalities" - 1 climber, 1 bomber, 2 builders, 2 bashers, 1 digger
8 "Don't Steal Our Honey!" - 3 builders, 1 basher, 1 digger
*9 "Rock Is Mine" - 6 miners
*10 "Tiny House Living" - 4 builders, 1 basher, 2 miners, 1 digger
11 "Ride The Nessy!" - 1 climber, 2 platformers, 1 builder, 2 bashers, 2 miners, 2 diggers
12 "Lemmings Join The Circus" - 1 platformer, 1 miner, 1 digger
*13 "Internal Head Trauma" - 1 bomber, 1 blocker, 1 builder, 1 basher, 1 digger
*14 "Dreaming Of Cyberspace" - 3 climbers, 2 floaters, 2 bombers, 4 builders, 1 basher
*15 "Mandatory Safety Meeting" - 3 climbers, 1 bomber, 1 blocker, 1 platformer, 2 builders, 2 bashers, 1 digger
*16 "The Allocation Strategy" - 1 floater, 1 bomber, 1 platformer, 2 builders
17 "Saving Tide" - 1 blocker, 12 builders
*18 "Schism In The Ancient Society" - 1 climber, 1 floater, 4 builders, 2 bashers, 2 miners, 2 diggers
19 "White Rabbits In The Snow" - 1 floater, 1 bomber, 2 platformers, 1 builder, 1 basher, 1 miner, 1 digger
20 "We Love Wafflems!" - 1 builder