it CAN be done without removing the bumper....but i really wouldnt recommend it... you risk scratching your bumper around where the headlight is (ask me how i know!)
really is a piece of cake to remove the bumper especially with a pair of helping hands, lay down a rug/piece of carpet on the floor across the width of the car and the front just in case it does drop and so you have somewhere handy to 'lean' the bumper just incase you forgot to disconnect anything like foglights, or for when you have to disconnect your headlight washers
repairing the headlight lugs is a piece of cake, my advice is go slow with removing the material and constantly try fitting the replacement piece into the slots that are on the headlight - you dont want to remove too much.
i found a few dabs of superglue help too along with the screw and then pop it back in.
(also, if its the bottom two lugs that your replacing, make sure that the nut on the lug is out the same distance as on the original one as this will affect the alignment of the headlight etc, dont bother trying to turn the nut after you've fitted the piece to the headlight as you'll risk snapping it off again, best to use a socket and hold the plastic piece in a dish towel in your hand and tighten/loosen as necessary)
good luck!