The answer is 10 rounds. This was one of my longest little league battles so far. The different was just a little detail that led to my win. Counterspell made it highly unlikely to battle against magic monsters, that was a hypothesis for my strategy. It's a Silver-League Tournament.
https://splinterlands.com/?p=battle&id=sm_IU933hrtRmUOQ7bDCUyL
As you can see, we both chose water with Keyla. I opted for a shield monster in first position, the enemoy for a self-heal monster. Neither of them got anything done until the end - the important stuff went on in the back lines.
And here's the detail - Since a lot of both our monsters had 4 health, except for the last one, the Opportunity ruleset would have all monsters go for the first one in second line - that's why I put my martyr there. The enemy put there Tide Runner in second.
Also, I had the Mandarin with Triage, healing the sneaked up on monsters - but the enemy chose the Merdhampir, which is an equally great choice, since it's Lifeleech combines great with cripple, having him go up in health with each attack.
As you can see, my martyr is almost done - so is the enemies tide runner.
So, starting round 3, I already had 2 boostet monsters. Meaning, that the enemy would go next after my third monsters, avoiding the tide runner who now had 5 health, and going for the Sethropod who I put there due to his high amount of armor - but the Merdhampir just laughs at that and gets the health down, anyway.
A good idea of the enemy was also to boost the Pelacor - that made it really hard for me to take him down...
...he avoided a few attacks and easily takes down the Sehtropod. But in Round 5 I finally get a hold of him.
But he still takes down my Mandarin, so field heal is out of the picture now.
Still, in Round 7 he's out of the picture - the Tide Runner as an Epic is allowed to attack first and takes him down. In the following round, the Bandit and the Runner take down the Merdhampir as well, before they combine all their effort to kill the Monk in Round 10 - there was a lot of missing in this game :-D
I hope you enjoyed this insight in strategy, and that it might help you in the future. Any tips and thoughts are very welcome!