Please, is there a way how to overclock the GPU clock above the BIOS limit of the card, without flashing the card?
No.
If the BIOS flashing is the only way to go, is there some nice tutorial how to perform it? What are the risks?
There are several threads in this forum on it using various ways; Using WINE, using FreeDOS on a bootable USB stick, etc. Just poke around.
The risk is bricking your card if the flash fails for whatever reason.
cent