It's probably possible, and the fights overall are quite easy even on the hardest level - that said, there are some fights near the end which will be a bit tougher. Still potentially doable, but might require a bit more effort (I personally haven't tried this since I like to get the best weapons for completion's sake).

Anyway, the first thing I would do is check out the major shops - first Sender Station, possibly Anachronox, and if there are still weapons missing, check out the major shops in other places (Haephestus, etc.). From memory, most weapons are definitely purchasable from shops in addition to finding them in the world, and it's not like you're ever short of money in this game. If you still have party members at a tier below the second-to-best, then you'll be guaranteed to find at least SOMETHING better.

Apart from that, one of these walkthroughs should point out where you can find them in the game world: https://www.gamefaqs.com/pc/196605-anachronox/faqs. It will at least save you having to scour the entire game world yourself - but still check shops first (or at least on the way to other places) as the walkthroughs are not 100% correct for shops (they're definitely missing some items/weapons).

OK, now I have the following weapons:

Democratus: Cyclic Sensor Array - best according to https://www.gamefaqs.com/pc/196605-anachronox/faqs/23678 but the planet is still grumbling and wants a better one.

Paco: Tumbleslam - also best but he also wants a better one anyhow.

PAL-18: Cordicorps Shockclaw > "Leave PAL in the Moon Burger for 4 hours" real life hours!?! I can't leave the shop without him.

Grumpos: Stargent Enerstrike

Boots: StarGent Handcannon

Rho: Tesseract Impactor

Stiletto: Stargent Bladerangs

AND I finally met Roweidekhalicon in Rowdys at Sanders Station. He tells me to head to Detta's fortress. Do you think, I can give it a try?

It's been so long since I played that I'm not sure how good those are. But I can tell you that I never bothered getting PAL's weapons from the moon burger - that's just a pain in the ass, even with fast-forwarding the time using the cheat.

I'm pretty sure (though could be mistaken due to memory) that you can get PAL's weapon in one of the shops (or possibly a better one?). Either that or I completed it with PAL's weapon being less than optimal.

I think it's definitely possible to beat the game with sub-optimal weapons since you can always just use lots of Mystech. From memory, there's at least one fight near the end where Mystech is the way to go. Mystech weaponry is not dependent on your standard weapons, you just need enough energy (which you've probably saved up over the course of playing - I had tons of glodents/batts/etc. by the end game).

Yes, you were right, in Detta's bedroom is a merchant who sells nearly every second-best weapon in the game.

Thank you for your help!

Now after I've seen the hole game, I must say: gameplay and the fighting was really strange, I didn't understood it till the end. But I loved the setting, the characters and the story.

No problems, glad to see things worked out for you.

Yes, the fighting was definitely not the game's strong point - luckily it's not required to fully understand it in order to trounce 99% of fights in the game. The most difficult fight is against that crazy character in the Mystech tunnels (he's only there after you go back to them, and it's entirely optional - I can't say what the rewards for it are since when I last played it, the game would crash every time partway through (this should be fixed with GOG's version)).

It's a shame Mystech was pretty much unnecessary for most of the fights as well, especially considering what a big deal is made of it.

Agree with you on setting, story and characters. Also I think they did a great job graphics-wise considering that the engine they used was already outdated for the time, and the level design was mostly believeable as well. For me it's definitely in the "best games most people have never even heard of" category - I discovered it prior to GOG existing but still well after it first came out.

Apart from the combat, the only things that bugged me a little was the backtracking required for certain weapons, and the crazy effort required for some of the others (Moon Burger - never could get PAL's weapon from this; Paco's best weapon from Bipidri photos - very easy to mess this up and it's kind of annoying, though I've done it a few times now).

Luckily for some of the other more annoying weapons - where you normally need a certain character to be present - you can kind of cheat using the ctrl key (IIRC) - if you hold that key down while clicking, you can pick things up as any character, such as those books for Rho's abilities, or the "hot" stones for Paco. I can't remember how I actually discovered this, but it defintely works (though I'm not 100% if it's ctrl or some other key).