In a past game (in which I scummed to fulfill the quest), playing as an archmagi, I got a very awesome robe from Melinda's father (Conclave Regalia, or somesuch. Was supposed to be what ranking members of the -you guessed it- human Conclave wore. Made spellpower rise a lot, among other things). So it's not always crappy.
In this particular game I was able to finish the quest because I had wisely invested 4 dots in explosion expert (thus making me able to hurt several cultists in every bomb throw), plus I had gotten lucky, and found an awesome 100 damage artifact staff on level 1 (which allowed me to deal a lot of damage to cultists while my bombs reloaded). Without the staff I'd likely not have achieved it, as while fighting the next to last cultist was what allowed me to deal a coup de grace . My golem wouldn't have reached him in time, and I still had to wait three turns for my bomb to reload. In fact, in a previous game with a very decent alchemist with a strong golem and strong bombs, it WAS impossible. Bombs have a too large reload time to be useful.
I think it'd be doable for an alchemist even without the unique staff (provided a decent-enough non-unique, though), if he had invested heavily in the staff combat beforehand (I hadn't. I had been investing heavily in the healing light spells I got from an anorithil).
Maybe it'd be possible to preserve the same build by buffing up just the barrier spell, of the healing tree (at first, that is) and of the stone tree, invest three dots in extract gems, and then one in each talent up to gem portal (imbues are nice, but you can make do without them for a while). This would mean an investment of 6 + (3 + X) where X is the number of points you wish to buff up Barrier (I think three would be nice, which would mean 12 points.) Which means that, of all the guaranteed generic points you'd have gotten by then, you'd have.... 8? left to invest in staff combat in order to make it a viable cultist killer? I think four and four in each of the two useful staff combat talents should make it worthwhile...