Thanks for the feedback!
If you're talking about the Watcher Above (the green eyeball), it is technically optional. You can explore the underground caves without the ability it's defending, you're just going to have a very short line of sight. Pushing forward to the double jump would make avoiding its projectiles way easier. But if you don't have it, the best way is to watch for the moment it stops and quickly put some distance between you, so you have more room to see the projectiles coming and jump over them.
Also, if you went left instead of right at the very beginning to collect the item there, you can get the gun early (otherwise you need to wait for the double jump to get it). It may or may not help, depending on your playstyle: it's a ranged weapon, but it also consumes a lot of stamina and may leave you vulnerable.
Hope you stick with it! ;)