Remove tight screw in expensive robot?

I'm trying to remove a couple screws in my two AIBOs (SONY AIBO ERS-311 and SONY AIBO ERS-312). I got one out of the 312, but the other is TIGHT and if I wrestle with it much more I'll strip the head beyond use and the skin on my hands will be completely torn (I'm already hurting). The 311's screws are just as tight as the remaining screw on the 312. I don't know how I managed to get the one screw out of the 312, it was pretty bad, too. I had my boyfriend try and he can't even get the screws out. The screws are on the robots' heads and the heads are made out of plastic. I don't know what to do without scratching/cracking the plastic and without damaging any electrical components inside (don't want to use any lubricant, don't own any anyway that's meant for screws). Suggestions?