hi!
I cant clear the level with spinning platforms. As far as I understand I need to get that green glowing hat to proceed to next level (and to finish with Sashas mind), but it is out of reach - no matter from which platform I jump - I cant reach the group of platforms where the hat is located.

You don't need to reach the hat. However, you DO need to shoot the targets (which are also, concidentally, GREEN). Just target and shoot with your Psi blast power.

The hat is just to replenish your psychic life.

hmm...

then I dont understand how to proceed with the game. How to finish that shooting gallery. I think that I have cleared all levels, but still every time I talk to sasha, hi tells me to "kill them all".

I should probably be more specific. Actually I have cleared already his mind. Now it is when I try "to face my inner demons", and dive in my own mind by the means of that huge device "braintumbler" or something like that.

I hope that my explanation makes sense - to understand where exactly I am in the game.

p.s. im still curious how to get on those top platforms in "spinning platform level". because besides thet green hat there are also some figiments to collect or whatever they are called.

Okay, spoilers ahead.

The first time through, you'll know when you've completed Sasha's shooting gallery because he'll automatically boot you out of his mind. But you say you've completed it? I think you mean that you've completed it, but want to get the rest of the figments, emotional baggage, etc. Much of that stuff you'll have to come back and get later, as you may not have the tools and psi powers to get them at this point. For example, those high platforms you need to learn how to levitate first.

So get out of his mind (if you're stuck in the shooting gallery, whiff the smelling salt from your inventory) and then walk up to the brain tumbler in Sasha's lab - and you get to enter your own mind.

Hope that helps.

Thanks for support!
I used the smelling salt and entered brain tumbler for second time - apparently I had entered wrong doors the previous time, because now I appeared where I had to - in Rez's own mind.