The short answer: Damage to enemy champions, KDA, vision score, CS, and gold. Those will get you the S.
The long answer: what's difficult about Jarvan is that between levels 9 and 11, you start finishing some tankier items if you're playing him properly for teamfights. That's not to say that damage builds are bad or wrong, but late game you're going to need to be a tank. It's common for melee champions to have to build that way due to how close they have to get to do anything. It's perfect for Jarvan because his combo literally puts him on Teamfight Ground Zero. The switch is difficult because you go from this high-burst damage sort of assassin to a tank that dives into fights and has to deal with the fact that you're the closest one to the enemy team. You have 2 options: kill them, or tank.
"Why are you telling me how you think Jarvan should be played? I already know how to play Jarvan!"
If you're building him as a tank, you're sacrificing damage BIG TIME. That's going to make it extremely difficult to get that S. Early game, he's kind of an assassin in some ways, especially if you're taking electrocute, so it's tempting to think you can always blow people up at any stage of the game. Regardless of how he ends up mid to late game, early Jarvan has high burst damage, armor shred, and a decently-long engage range. That's straight up an assassin. The damage falls off a bit late game, so landing your CC usually only matters late game if you're with your team. Even if you're building damage, that all-in can get you killed if you're not 100% killing your target. The fact that a target can flash your ult before you hit the ground and prevent damage makes that a bit difficult.
I personally just like to win the game. I generally do a build with all items that scale HP like Cinderhulk, Titanic Hydra, Locket, Sterak's Gage. All of those things have a health ratio on them, then your W does as well. The build has damage and tankiness, definitely capable of getting an S while still being a teamfight tank. Of course other items like Randuin's Omen, Knight's Vow, Spirit Visage, Adaptive Helm, etc make it in there as necessary. Against squishies, I might do Black Cleaver or Duskblade instead of Sterak's Gage, but you'll have to build it waaaay sooner, like 2nd after Cinderhulk but before boot 2. Sterak's Gage is usually the first item I cut if I need to deviate from the build. It's really only good if you're winning and have a level or 2 on most of the enemy team since it scales with your scaling base AD. I think Warrior Enchantment is shit because that item has no abilities and the stats on it are pretty tame compared to every other jungle enchantment, but you can still build it if you just want damage for the S.
Keep in mind that getting an S with a build that isn't conducive to helping your team win teamfights can also be a build that isn't conducive to winning the game. You may be able to blow somebody up with a full damage build, but you can also get Cho feasted, Eve ulted, Jhin 4th shot, or Camille backflipped and die because your damage build probably excluded the health and damage you need to just win teamfights and win the game. So if you want to do a damage build instead of tank ,even after all those damage items you think you might want in order to get the S, you still have to jump into fights, land all of your abilities, hit a bunch of basic attacks, and not ruin your score in the process with your squishy self.
. Getting an S in a sub-40 minute game is pretty hard in most cases.
