It does check sexuality and sex attraction, yes. You also can't be rivals, and they have to either have opinion 45+ of you or have the "Budding Romance" opinion modifier.
Things that make this more likely are:
1. Your opponent is Lustful.
2. Your opponent has no lover.
3. You are Attractive or Groomed.
Attractive is congenital, as I'm sure you're aware. Groomed can be gained during upbringing (unfortunately I don't know the mechanics). During adulthood I only know of two ways: one is harassing them with the option available to bearers of the family bloodline, the other is a rare event that can only trigger when you are on either the Family or Seduction focus.
Love is a Battlefield is a pretty hard achievement to get, I find. I got it randomly while playing as usual. Basically whenever you get an option to do something with someone after a duel, take the friendly approach.
Since this event does not appear to be possible when you are rivals, it can be hard to find appropriate dueling partners. My recommendation for that would probably be to play as a Zealous Catholic and duel Excommunicated Catholics. You can even send them a gift beforehand to increase their opinion of you.

The same tactic should work if you are a Zealous Muslim, except then you'll be targeting Decadent rather than Excommunicated Muslims. If they combine this with Lustful it should help you out a fair bit.
Just remember to check that they have no lovers before you pick a target. This was usually not a problem before 3.2, but with the new adding of random lovers that has changed a bit. If you try it out and find that all or most of your potential targets have lovers, it might be worth going back to 3.1.1 and playing that with AI Seduction focus turned off.
PS. The requirements and bonuses I posted above are correct as I got them from the game files themselves, but I don't know if they are the whole story. The chain of events that lead to the achievement is not one that you can easily get a complete grasp over just by skimming. If you want to do more research on it I'd recommend searching the game files for "achievement_love_is_a_battlefield" (the flag that is added to you when you get the achievement) and work backward from there.