Here is the full list of all 12 Lemmings trophies - there are 8 bronze, 3 silver and 1 gold.
Save every Lemming possible
Complete all Mayhem levels
Complete all Taxing levels
Beat 3rd Time Lucky in under 1minute 30 seconds
Make a clone that can float and climb
Complete Teach me Climbers and Floaters in under one minute
Blow up 100 Lemmings
Complete all Tricky levels
Set off 100 digger Lemmings
Send 1000 Lemmings to their death
Build 100 bridges
Complete all Fun levels