Try not to shoot too much
Shooting is obviously part of the game. That said, you need to be wise about how often you shoot. This is because you need to deal with enemies, and if you shoot, then they'll know where you are. But, if you can stay out of sight, then you should be fine.
And in early levels, you just need to worry about traps. So there's no need to think about enemy awareness (yet). Now, you need to see, so definitely do what you got to do to see. But, after a shot or two, then go ahead and test yourself and see if you can manage.
Also, if you jump, you'll be able to see yourself too. This is your safest bet since you aren't firing a projectile that could accidentally land near an enemy. So, if you need to see, then I'd prefer jumping overshooting. With all of this being said, if you feel like you can take out your foes with no issue, then, by all means, blast away with that gun. Just be careful.
Be careful when jumping
I say this because when you do a hop, you don't stay in place. In many games, it requires a combination of the jump button and pushing the analog stick/d-pad forward. However, in Invisigun Reloaded, pressing the jump button automatically makes you flip forward.
This can certainly be helpful as you don't need to worry about slipping up on the analog stick or anything. Because let me tell you; there's nothing worse than when you think you have your thumb on the analog on your phone, only to quickly realize you accidentally slid your thumb off of it and resulting in death or other things.
The bad thing about this automatic jumping forward feature is that you may easily bump into traps if you aren't careful. It's really just a matter of getting used to it. As we mentioned before, jumping is a great way to see yourself for a second to help gather yourself. If you know you're near a trap, then fire a shot before jumping if needed.
Each character has their own abilities
OK, so we talked about jumping a bit, but this ability is centered around the character you start out with which is Selene. She is the only capable of performing the jumps. But, there are other characters that you can use, each with their own special abilities.
Aether, the other character you can use right away, has the power to use a ground pound move to eliminate enemies and obstacles for example. But there are others that can be unlocked too (although you need to pay $.99). Some heroes let you use slashing abilities while others let you teleport.
Try testing a couple of them out to see which one you like best. It's always fun to experiment with different characters. And with Invisigun Reloaded being as tricky of a game as it is, having these powers at your disposal could really be helpful and you may find some more useful than others.