Hi there
IMHO I think the spider is the most difficult fight in the entire game mostly because of the restrictions on selection of the units.
(no scratch that, the most difficult fight I had was with that elven princess, instead bringing her antidote I insisted that she should rest out, boy the army she assembled, just skeleton archers 42k+!! 5 stacks of 8k each plus regular infantry.)
Anyhow, see what spells you have and then increase your magic school accordingly. One good damaging spell of the 2nd level will do nicely. I don’t remember how many hp he has on normal, my guess around 18k so you should have him down in less that 15 rounds for the achievement.
Myself I’m at the end with my no loss imp. 6 fights to go, it would be a breeze if I didn’t have to use the allies with their limited spells assortment, no dispel, no res for some, no gift, this feels like boxing match with Mike Tyson but you can use only one hand and no biting so better make it count.