I don’t exactly know why, but sometimes ramming them with a stingray insta-pops them. Usually it only works when they’re low on health, but sometimes they die anyway. Maybe you need to hit one of their eyes.
I feel the pain for the challenge dude. I created a thread about it and some of the other inane (and insane!) challenges a few months back.
As for the vehicles, equip an Excalibastard and have it on hand, get a rocket pod vehicle, use the gun to score a crit and explode the Shuggarath with rockets.
I can probably dig it up. They aren’t personal challenges I made up, it’s just the ones that I feel are WAY too difficult (by difficult I mostly mean time consuming or just don’t make sense) and should be avoided when trying to prestige. I’ll edit this post if I find it.