Firstly I think level 27 is a little early for the Driller. I think I am level 29 in my current game and I haven't taken on the Driller yet. I don't think you said what difficulty your game is. Anyway, I think your team is a little too 'tank' orientated. The reason why you have four units is simply because the Driller likes to use his machine gun if you have two units in the same row, and as there are only four rows, this is a problem with five units. What you need are units that do high damage and preferably without retaliation. I usually use Royal Snakes for this reason. Also, it's hard to go past Archmages as they have two useful skills: their Magic Shield, which can be put on your tank unit, and their lightning attack. So I would probably lose the Assassins and replace with Royal Snakes. I'd swap Dwarf Gunners with Archmages, and also only use one of Archdemons or Giants. I like Giants but I think Red Dragons are even better for this fight due to their ranged fire special attack.
So my team would be:
Paladins (mainly for resurrection - if you don't mind you can live without them)
Giants (or preferably Red Dragons)
Archmages
Royal Snakes
Hope that helps.
