When doing these for the trophy/achievement and 100%, play as Franklin so you can trigger his special ability to slow down time while driving (which is very helpful for lots of the Stunt Jumps). The recommended vehicle for the Monster Stunts is the Pegassi Bati 801 motorbike as you can do pretty much every stunt with it. However, some stunts are easier to do with a sports car.
When stuck at a stunt, use the same type of vehicle that is shown in the video. You must always land in a specific area, or even a specific spot to complete the Stunt Jump. If driving too fast or too slow, you might miss the target area and the stunt will fail. A neat trick to use is to quick save the game before every stunt jump. After loading the saved game, you will be sitting in your car or bike at the exact same spot where you saved the game. This allows you to never lose any progress if you die or destroy your vehicle.