Speed Trophies are earned by completing the Trophy time on a level. In order to do a speed run you must have completed the level at least once. When you go to replay a previously completed level there will be a gold stopwatch somewhere near the beginning. Attack it and the time trial will commence. There will be two different times listed on the time trial. The faster of the two times will earn you a speed trophy. Some of the trials are not too troublesome but some can require near perfect platforming jumps. Just replay the level over and look for shortcuts and ways to decrease your time. Avoid hovering if you can as you go slower and if you lose momentum hit the attack button to speed up (this can be particularly helpful on ice levels or when you are going uphill). Other than that you will generally want to avoid running into enemies, if you bubblize you will have to restart from the beginning of the level. Generally speaking you should be holding down or constantly.