This may sound difficult, but it's really just frustrating on a few levels to rescue every lemming possible. You will need a total of 1404 lemmings saved across all levels.

See this thread for the amounts needed and videos for completing every level in the game: Lemming Leader Guide - PS3Trophies.org

Start up a level that has 100 lemmings. Pause and increase the rate to 99. Lead them to whatever will kill them. Continue this until the trophy appears.

See 'Lemming Leader'.

See 'Lemming Leader'.

This is Taxing Level 1 (3rd Time Lucky). When the third lemming comes through the entrance, pause and increase the rate to 99. Have the 3rd lemming dig so he can pick up Basher and Floater. Give the other 4 lemmings the climber skill. Bash with the first lemming on top and build a bridge to reach Basher. Make the other lemmings floaters. Finally, bash with the lemming on bottom so he can reach the exit. If all goes well, you'll complete the level fast enough for the trophy.

See 'Lemming Leader'.

See 'Lemming Leader'.

This can be gotten on Mayhem Level 3 (Lem Lift Us Up). Have a lemming climb up and grab the floater skill, build a bridge to reach the cloning machine and clone himself. The trophy will pop up as soon as you've cloned the lemming.

You'll probably get this while playing through every level. If you don't, find a level where you had to build bridges and build as many times as you can. Restart or quit and do it all over again. A good level to use is Trial Level 2 (Teach Me Builders And Bashers).

Same as above, you'll probably get this while playing through regularly. If not, go ahead and find a level where you had to dig and dig as much as possible and quit to do the level again until you get the trophy. A good level to use is Trial Level 4 (Teach Me Digger And Miner).

This is one you'll have to repeat over and over again on any level with the bomb skill. Blow up as many lemmings as you can and restart or quit the level and do it all over again. A good level to use is Trial Level 3 (Teach Me Bombers And Blockers).

This is Trial Level 1 (Teach Me Climbers And Floaters). Pause at the beginning of the level and increase the rate to 99. Give every lemming climber skill and then floater skill when those are collected. You'll complete the level fast enough.