Only certain characters come standard with a wrench. Your second partner in the first level, Jock, has this ability. When you see a smoking object, switch to a wrench carrying character with in story mode or in freeplay, and press to fix the object. Also, if you see a wrench on the ground, any character can pick it up with and fix smoking objects. To check to see if a character comes ready with a wrench, press to see what they're carrying.
If you're looking to get this achievement in a hurry, go to Movie 1 Stage 5and fix the engine that powers the lift in the center of the first section. This engine is a bit different than the other ones throughout the game in that it works for about 5 seconds to power the lift and then breaks again, allowing you to fix it over and over.