First off, why the game requires you to play through the game a minimum of three times I have no idea. Whoever at Armature thought that was a good idea, you suck dude.
Anyway, your first playthrough I would recommend the following:
Play through the game as normal and follow the guide for the Blackest Night Suit (Zombie Suit) so you can utilise this on your next two playthroughs. The suit stops you taking any damage including bosses and Joker gas meaning your playthrough won’t be slowed down by conventional deaths (you can still fail on things like bombs exploding or hostages dying).
Whatever boss you choose for last really doesn’t matter, just make sure that you collect all pieces of the Blackest Night suit before completing this playthrough, although choosing Penguin last means you naturally end up outside the Arkham Wing entrance after defeating him but regardless, the order doesn’t technically matter.
Note: Just remember to pick up the Batsuit Cowl piece after finishing the last boss-specific collectable (Junction Box, Hostage, Present). Batsuit pieces carry over playthroughs so only need to collect it once. Note Part 2: You’ll probably find the "easy" collectables like Joker Teeth, Bird Cages, and Black Masks just by going through the entirety of each area, but these can all be saved for the big final playthrough if you miss any.
Second PlaythroughThis playthrough is all about speed. Finish the game as quickly as possible. You can equip the Blackest Night Suit immediately (on the rooftops while you’re chasing Catwoman) so make use of it. To end fights as quickly as possible, use the beatdown combo (B, spam X) and counter whenever necessary (normally you can get pulled into the finishing animation before anyone actually hits you).
Don’t concern yourself with anything in this run other than just completing the story. To be on the safe side, aim to beat the boss first in this playthrough the one you defeated last in your first playthrough.
Final (Big) PlaythroughOkay so now this is where the work comes in. To be able to find all the collectables, you’ll need 99% of all the upgrades. To ensure you don’t need a fourth playthrough, map out your route to defeat your remaining boss and get your final Batsuit cowl piece. It’s worth waiting until you’re ready to end the game (I.E before you go beat your final boss or go to the lighthouse area) to go round collecting everything.
I’d also recommend searching by area (Admin, Industrial, Cell Blocks) rather than by collectable type. That way you’re not running back and forth between the areas (fast travelling would make this game way easier).
A guide for all the Batsuit pieces is here:
A guide for all Gauntlet upgrades is here:
Cell Blocks = 0:05 (need to be chasing Penguin after defeating Bronze Tiger and have Batclaw)
Admin = 1:02 (Need Line Launcher and Tightrope upgrade)
Industrial = 2:12 (need Batclaw and Shock Batarang upgrade)
A guide for all Armor pieces is here:
Cell Blocks = 0:06
Industrial = 1:19
Admin = 3:25
A guide for all RUSH upgrades is here:
Cell Blocks = 0:06
Industrial = 1:01
Admin = 1:33
A guide for all case files is here:
Cell Blocks
Industrial
Admin
As posted by TrueHelp, there is one random upgrade for the Gel Launcher called Proximity that you can find just before going into the room with the 3 big generators you need to shut down to fight Black Mask. If there’s one thing you’re missing, this is more than likely it.
You won’t grab your final collectable until you’ve got the last of the boss-specific collectables done and got your final Batsuit cowl piece.
I just wanted to write this all down because I lost a lot of time on this game backtracking and wasting time on my first playthrough.