Every time I try and fight the second boss I manage to get him down two his core 2-3 times. However, afterwards he roars and seems to become invincible (he starts to flash). No matter what I do I can't get an more bones to fall off after that.
He's not invincible, just that in Fury/Rage/Whatever mode (when they flash black) they get certain buffs and such, and basically instead of breaking off pieces, it all comes off as one, just keep attacking and it'll all come off at once really.
I find that I can get it down faster if I simply go for the blue core and ignore the pieces (they generally just fall off anyway). Keep attacking the core and run away (and slurp up a green drink) when it starts to glow. When it all goes back together get inside and keep hitting the core until it eventually turns black and then gold.