I think we figured out that you definitely can't kill him, IIRC Cave_Johnson poked around the .exe and he's unkillable.
I don't think I hardconfirmed it back then, but these days, the source is readily available and I looked.
He has 30000 hp.
And he has 30000 regen per tick (didn't bother to check if/how that's scaled, and his tics are 7 I think but I didn't check against what time unit - with values this high, it shouldn't matter.)
So you need to do some really fast insane levels of damage or he will heal it all back long before you can finish him. I strongly doubt any normally-available means can do that much damage, quite possibly not even typical crushers. A crusher set to do extreme damage, perhaps, but such a crusher would instantly kill any player at any level unless they have true invul, since player hp and regen are nowhere near this level.
He is flat-out immune to several types of damage but not all. Which is purely academic unless you've found a way to do thousands of damage per frame with at least one of them... so ultimately, if you do catastrophic damage with one of the right types of damage, he should die. The question is, can any usable means of doing damage without editing the game meet that kind of sheer DPS? Doubt it, but I'd be happy to consider any speculations.
Side-note: Those pesky blue elves in Q6 ARE normal-immune and fire-immune, but also have other things that they're not immune to, and they don't have insane regen.
