For this achievement you only need to finish 5 of the 15 races, but you'll have to complete all 15 for one of the suits for "Fashionista". There are two different types of races: The first one you can just tap to zip to each checkpoint. The other has two different checkpoints, one where you automatically zip to it, and the other you'll have to do whatever you can to get there, being running, swinging, running, etc.
These are timed and can be somewhat challenging on Super Hero difficulty. You can change the difficulty to make any of the side missions easier. Only change the difficulty AFTER you've completed the story. Changing the difficulty only affects difficulty related achievements.