I haven't seen Death Note but to my knowledge Light requires his target's full name in order to use the DN on them, so Sherlock goes down almost immediately given his world-wide fame. Moriarty tends to self-sabotage due to his enjoyment of toying with his enemies so Batman defeats him pretty handily (given that he's got lots and lots of experience with a wide variety of enemies that do that, and access to much more modern tools and equipment than Moriarty knows how to counter). Light would eventually be found out and then defeated by L and Batman, unless he managed to figure out Batman's identity. That leaves L and Batman vs Kira.
Given that they have time to investigate beforehand, Batman probably knows going in that Kira's got a definite kill-radius in close proximity to his victims, so he'd hang back, probably test it with a few batarangs (which would get taken out by KQ). Batman would then strategize, throwing multiple batarangs together, observing what happens to them when they approach Kira (specifically, how close do they get before being stopped- showing Bats what Kira's radius is, even if Bats doesnt know what his ability actually is). If one of those batarangs was rigged with knock-out gas, then it detonating (either from KQ smacking it aside or trying to explode it) would probably incapacitate Kira, since KQ doesn't have any specific defenses against gas-based attacks. Even if KQ managed to blow the first one away with pure speed, it would give batman an opening to keep attacking until Kira succumbed.
If they start too far away for Batman to use a batarang, though, then it's a much more dangerous fight. Sheer Heart Attack is effectively unstoppable, but it's important to note that SHA is not as lethal as KQ's main ability. Jotaro survived SHA detonating point-blank and was in good enough condition to catch up with Kira and Koichi afterward. Batman is in better physical shape than Jotaro and wears body armor, so SHA would not necessarily kill him- and after that first blast, Batman would know he's also got an invisible enemy to deal with, meaning he needs to deal with Kira immediately before dealing with this new enemy. Given that SHA also seems to have more interaction with its physical surroundings than other stands (actively smashing through obstacles, leaving tracks on the ground) if batman were to throw down a smoke bomb then he might be able to track SHA based on how it disrupts the smoke.
But then there's Bite The Dust. Kira gets a second attempt at the day, now aware of Batman's initial tactics and ability to evade SHA, if only for a short time. If he tries SHA from a greater distance, he would still run into the issue of batman wising up after the first blast and then being constantly on the move to avoid it. It's possible then that batman, by observing his surroundings, could witness SHA's attraction to heat and exploit it, even without fully understanding SHA. Given than it's got his full attention here since Kira's not around, it's much easier to observe and figure out how to avoid SHA, even if he needs to take some damage in the process.
If Kira tries to fight him directly after (let's say he brought a gas mask with him this time so no knockout batarangs work), then Batman would exploit his surroundings- namely SHA. By lighting fires with his explosive batarangs, Batman could lure SHA back to Kira- leading to Kira either getting self-detonated or having to recall SHA, either of which solves a problem for batman (the latter of which revealing that it was an ability of Kira's and not a second enemy). Given his arsenal and skillset, I think that Batman would still win here.
If Kira had unlimited BTD however, there's no question he'd win. Eventually, he'd figure out a strategy that successfully killed Batman.