The Bosses require some unusual cunning
I did the spider on lvl 30, the driller on 38 and he frog on lvl 40.
In order to do the properly, you need a lot of firepower, which as a mage, is very scarce, and using spells on the bosses is simply a waste of mana, which should be used for phantoms to resurrect the fallen troops.So in essence, you need to rely on your attacking units. In my case those were the Knights and the Paladins. Since bosses mainly inflict physical damage, make sure you stock up on +phys resist stuff and put stone skin on both troops that will tank the boss.
Spider: Knights on the left, Paladins on the right, T-rex, Archmagi and Demonologists deal with the spiders he summons, and the knights help occasionally. The boss itself doesn't do that much damage, so the standard tactic: Knights with Stone skin and Magic Shield and Paladins + Stone Skin works perfectly. If you have any physical resistance boosting items, use them.
Driller: now that boss required some thinking. His gun is awful, hits everything in a straight line. This is why I did it only with 4 (!!!) troops: Knights, Paladins, Archmagi, Inquisitors. Knights and paladins hack away while the archmagi and imquisitors (both with magic damage for the droids he summons, as they are vulnerable) attacks the boss or the droids he summons. When he summons mechanics, dwindle them down to a like 5-10 units and leave them be. Finish off the boss and get resurrecting.
Dersu frog: Now that frog's awful. Her spit is poisonous, and it hits very hard. If you have healer's jacket, put it on. Forget about other bonuses. Having healer's jacket or anything that bossts poison resistance is very important. The frog itself isn't that hard, as it doesn't hit for much, especially if you do the dual tanking tactic with stone skin.
I got carried away and forgot to do a frog screen, but in any case, here's my stats after the battle if it can help.