Attack Skill +1 или Basic Archery?

You need to acquire a helmet, I think. Moreover, the mission description states that we won't have time to conquer everyone and need to seize everything we come across.
.....

I don't remember for sure, but I think I completed this mission like that.
I ignored the Barbarian castles, built up my own completely, and then ran past the Barbarians to the Warlock with only my own army. Maybe there were some other tricks, but I don't remember. There's a teleport scroll somewhere. Again, I don't remember exactly where. I defeated the Warlock without any problems with my own army in about 3-4 weeks. The result isn't ideal, but it's something. In general, you could probably do it even faster with the same scenario + capture a couple of Barbarian castles and buy out their treasury. The Barbarians are also killable, in principle, but it's too much of a hassle, so I just ignored them.

Well, while I was writing, Querty already answered and provided a more accurate solution...