Lies Of Astaroth

All credit for this method goes to MemoriesOfFinal.

While this achievement may very well come to you eventually through normal play, there is a very easy method you can use if it does not. It does require a tad bit of luck, but once you have it set up, it's hard to fail.

What you will need:
An invasion in one of the first two maps
Two Flood runes, preferably level 1 (level 0 being the first)
Two weak Kingdom cards at level 0, Shieldmen work well
One strong card of any type

Every day you'll get an invasion in one of your unlocked maps, so the luck based part here is just waiting for it to be in one of the first two. Get two Flood runes from the Temple (you can buy them for 4 blue scraps each) and level them both one level. Now you'll want to start the invasion fight, play both your Kingdom cards and keep your strong card in your hand. Once the two cards die (keep in mind they need to be strong enough that the opponent has time to put out all their cards before this happens), the Flood runes will trigger, and over the next few turns they will reduce all enemy ATK to 0. Now that the opponent can't do anything to you, all you have to do is keep ending the turn until the counter on the left reaches at least 51. At that point, play the strong card still in your hand to end the fight, and your achievement will pop shortly after. If you do mess anything up somehow, make sure you lose the fight or forcequit the game (guide button > start > quit game) so you can retry.

On a sidenote, this currently does NOT work in dungeon battles, but the devs said they're gonna fix that.

Here's a video showing the method:

"Exceed 50 rounds in one battle"
I don't think it counts in Dungeon or Tower, so may be only in Campaign (needs verification).

Not Sure if its a glitch, or because I have some incomplete maps, but I've not had any invaders for months now. I was beginning to think that I'd not get this one, until yesterday it just sort of happened.

I was playing 9-7-3 on Torment, and the victory condition is to eliminate all of the opponents cards. So I was playing conservatively, just matching the AI's cards instead of going all out, keeping most in my hand so I wasn't reducing the AI's HP by much.

This AI opponent has a lot of cards with Resurrection, and the randomiser kept bringing them back into play. By the time I had finished the match, it was up to round 55 or so. I had eliminated the same 3 or 4 cards over and over for most of the game, and only these cards since about round 40.

So there is an alternative to getting lucky with invaders - find a Campaign Map level with multiple cards with Resurrection, and get lucky with the game's RNG to get 51 or more rounds.

Hope this helps, just sorry I couldn't find a method without the luck factor.

Please comment if you obtained this in Dungeon, Tower or vs Thief and I will amend accordingly.