Learn when enemies spawn. The game becomes easier when you know what you're dealing with.
Always move! If you stand still you'll be dead in no time.
Learn to kite a group of SKULL I. They have no high priority since they will not kill you if you make smart use of the advanced movement mechanics. Kill SKULL I's when you have nothing else to do.
Stop shooting every now and then, because then gems will quickly float towards you.
If you are already a skilled player: leave SQUIDs alive! After a while they will spawn another wave of SKULL I's along with one SKULL II, which can give you gems. That way you can get upgrades early. Visit the Gems page for more info on farming gems.
If you fail to kill a SPIDER (or any other enemy), don't freak out! Just keep moving and find another target. If you lose speed then other enemies will kill you. Return to the SPIDER a few moments later.
See the priority list below. Generally this is a vague idea of what you should shoot first in order to stay alive. In some cases this list may not be perfect.
For fighting the SPIDER, shoot at it's head instead of the gem. It's head is the only hitbox.
The second hand upgrade has a pretty accurate shotgun-blast. Use this to take down SPIDERs and SQUIDs from a big distance.