Don't rock or tilt the hsf when installing it,(too easy to break or crack cpu) put it down flat into position, hook short side of retaining clip first (if there is a difference), use a pencil w/stout eraser, or a screwdriver, or needle-nose pliers (not the smooth-jawed one's), .......... or whatever it takes to safely hook the long/other side of the retainer over the zif-socket tabs, without slipping off and damaging the mb or other components........
It really helps to install the cpu and hsf into the mb before mounting the mb into the case.
If not possible, then ............... lay the whole pc case on its side and un-plug or remove any obstructions prior to installing/removing hsf.......... good luck!