Every time I start the first boss fight, i get this weird texture corruption as if the first boss is tied to a rope from the shoulders. How can I solve it.
For a picture, please see here:
http://i26.tinypic.com/2r3f1av.jpg
Installed the latest version of graphics drivers.
My system specs : Core i7 950, Gigabyte GA EX58 UD4P, XFX GTX 275, 6 GB Corsair 1600 memory, Enermax Revolution 85+ 1250W PSU, Dell U2711 monitor, Windows 7 x64

It's a known issue with the game. Not game breaking though, so don't worry about it.

So I guess no solution then :( ?!!

Not that I know of. I can't remember where I saw this bug mentioned previously as it was some time ago. You could try different renderers (OpenGL or DirectX) or you could try different graphical settings, maybe even just for the duration of the boss fight.
But anyway, it shouldn't be a game breaking bug, so you should be okay to continue.