Surprised you are even asking! I would say that needs a definite replacement. My Giro wasn't as bad as that and I have replaced it. Did its job though.
my main concern with that damage would be the joint with the bottom level of polystyrene... without seeing the helmet physically (and the inside) and looking at it, it is hard to say, but I know I replaced my helmet with this damage... but it did take me a number of months because of my location and the options available to me in the former eastern soviet states... (before you ask, a rock was thrown at me so saying no to sex with a drunk teenager! - and you think I don't know how to have a good time
That looks to me like a rare thing - a picture of a helmet where the polystyrene has crushed (and absorbed an impact) rather than split (and transmitted an impact). I probably wouldn't bother replacing.
Bingo!My noggin just got saved by mine today