All in all, this isn't that difficult. There's a couple of strategies that I would suggest in order to both make this easier and also to make then entire archenemy campaign easier.
The first thing I would suggest is to plan out what decks you are using to go up against the Archenemy. In my experience I've found that using Jace's deck, Realm of Illusions, is a good way to go. It has a good amount of illusion creatures that you can use to power up the Krovikan Mists that are in the deck and, because they get power and toughness equal to the total amount of illusions in play, you can make all of the decks you are attacking the archenemy with Jace's so that you can have multiple flying behemoths to attack the archenemy with. Also, if you've unlocked Lord of he Unreal then it's a good idea to make sure those are in your deck as well because he grants all of your illusions hexproof.
This sort of ties in to a second tip I would suggest. It's always a good idea to coordinate the efforts of the three players on your team so for this I would suggest either finding a couple friends to play with that you can talk to and plan with rather than relying on the AI to do what you want it to do (though in general it does seem to play fairly smart) or you can just control them all yourself if you have multiple controllers to use.
These two strategies should help you get this achievement without much hassle as well as get you through a fair portion of the archenemy campaign. Just keep in mind that you may want to change your strategy in accordance to who you are playing (ie: if you use three Realm of Illusion decks against Jace his Krovikan Mists will get powered up by what you have on the board as well, etc...).
As pointed out by The Globalizer in the comments, you do not have to be the one that actually takes out the archenemy (ie: deal the final blow), as long as one of your team mates does it it counts as you defeating them as well