Update: I was unfortunately not aware of Shamus Young's severe criticism of Fallout 3 available here to link in the original piece and I regret that. It dovetails rather nicely with what I've written and it's much better executed than my piece. I strongly recommend anyone...
Use your double jump to adjust your trajectory during a jump.
Explore alternative routes to bag all of the coins and track down that elusive star.
Checkpoints will allow you to restart midway through the level, so be sure to seek them out.