How Do I Earn the Time-Related Bonus At the End of a Level?

Solution 1:

What you need to do to earn the speed run trophy, is go back to a level to replay it. You can't ever earn the speed trophy on the first run. When you start a level a second time, you'll see a flying stopwatch with two target times displayed next to it. The time displayed on the bottom is the time you need to beat the level in to earn the speed run trophy. The time on top is the minimum time to beat to at least get the 6th electoon for the level.

To actually start the speed run, you have to hit that stopwatch.

From there, make your way through the level as quickly as possible, and without dying (if you do, you go back to the beginning to start it again). When you get to the end, you'll see a flag. Get to that flag under the target time, and you'll earn the speed trophy.

I've only tried a few of these, and they're pretty difficult IMO. Takes a bit of memorization of the levels and some patience.