Just throw the alien grenade as soon as they start coming. It will kill them all instaneously and you can get back to attacking. It takes about 3 or so cycles and you are on to the next phase.

I don't have any alien grenade. I collected the blue sphere but cannot get back to the cave without killing the alien - at least I could not find a way.

I attached a screenshot of the alien i mean.

Oh sorry, when you said "tenticle boss" I thought you meant the final boss.

I'm trying to remember how I beat him. I think I went a great distance away and just fired at him from a distance. I would keep an eye on the ground as the electrical balls go along the ground. When they would get close I would focus on jumping over them and then get back to shooting once they passed.

Since you said I was missing a weapon I tried again to find a way back to the cave and I managed to find it. Now I have the green gun which seems to be powerful enough to finish this boss (or so I hope).

Maybe I am wrong but I remember relatively small balls of electricity that slowly approach the character along the ground. You may have to do a slight run-then-jump to clear them. Rolling won't work as they will hit you. Maybe I'm remembering it wrong?

No, it is exactly how you described it but since the alien does not stop to shoot at me I will either run/jump into the next fire or hitting the next spark. So the game wants me to aim/shoot/jump/aim/shoot/jump and that pretty fast without getting hit twice (because after two hits it's already game over because the explosion in the first phase nearly emptied my health bar). Add to this that it does not seem to be possible at all to regain health using the flask while inside a battle - youi just don't get the time to do it.

Hmmm. If I recall I was all the way to the right on the area so the boss was a good distance away when I was firing at him. Also, you mention losing a lot of your health. Make sure you equip the items you find to increase your armor so when you do get hit you take less damage.