You can fire upwards in this game. Remember that to save yourself some trouble.
If you're ever in a situation where you're on a platform and it's inevitable that you will get hit, try to stand in the middle so that you won't fall off. It's not like Castlevania where you fly backwards when you get hit, but you'll still hop back a little.
Use your special attacks whenever you can. Not only are they useful for killing enemies but when you hit them with it, they will drop a coin that you can use for the mini-games.