Okay so I got it to work!
But I promise all I changed was attaching the three LEDs.
During the process the error led lights up shortly.
The power led stays on and the working led blinks.
The pullup resistor is not necesary.
Thanks for your help guys!
I tried it with another (small) ATtiny85 on a PCB with components attached and got this problem:
avrdude: stk500_program_enable(): protocol error, expect=0x14, resp=0x50
avrdude: initialization failed, rc=-1
Double check connections and try again, or use -F to override
this check.
avrdude: stk500_disable(): protocol error, expect=0x14, resp=0x51
and after some tries its always this one
avrdude: stk500_getsync(): not in sync: resp=0x00
During the upload only the power led is on.
This ATtiny already has a sketch on it.