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The Devilish Strike really does the trick. I remember struggling for about 5 hours trying to kill the Necromancer with a chain attack, and I didn't even use it at first.
With a magic-focused build, everything is different: in the first mission, I won the Dungeon in less than 2 months (here's a battle with the last demon around week 7:

). In the second mission, I defeated the Necromancer on the first try without any problems; I completed the third mission in just over 3 months (but there, Dark Magic is a must-have to get the garrison to the orange portal), and the fifth mission in 3 months, 3 weeks, and 5 days (there, machines are essential to defeat the golems/gargoyles). In total, it took 701 days (using the "u.s." - hero) to complete. I received the Dragon Arcat badge, and there are definitely areas where I could improve; maybe I'll try to get the Thunderstorm sometime.