Ok, I had to drill the screw to break it. It was very delicate and time consuming operation. But in the end the screw cap finally broke off and I was able to remove the battery!

Top screw didn’t move with iFixit Philips #000 driver. The metal is too soft and in the result the screw was damaged while still in place. Having nothing to lose I also tried #00 and #0. Any way to remove the stuck screw? I would gladly saw it off if I could.