Always head for the floating orb demons. When killed, they will drop valuable items!
Persistent wings are very helpful - they should be the first thing to spend your coins on!
Also, save your coins to unlock warp gates. They will let you proceed directly to the next boss and level.
When carrying the Clock, you aren't necessarily "unarmed". Always carry two or three grenades, so you can kill orb demons to get more items.
Use boosts and mystic grenades wisely, as they are single use items - they will be consumed on use.
Run to find out about the background story. Depending on who (or what) has been rescued before, the storyline will unfold and eventually get a surprising twist...