New Game Plus, or simply New Game+. is a feature that exists in many games nowadays. Usually, NG+ is available after beating the game normally once. In most games, equipments and collectibles usually carry over in NG+, allowing us to replay earlier sections of the game with our late-game equipments.

NG+ feature is implemented in Batman: Arkham City, Origins, Knight, and of course Origins Blackgate. In almost every game, counter icons are removed in NG+. However, this is not the case with Blackgate as counter icons are still there.

However, there are more differences compared to the NG+ of other Arkham games. In both Arkham Origins and Blackgate, unlocked gear does not carry over since most of them are acquired through the story.

There is no free-roam after finishing the story. However, if you select "Continue" rather than "New Game Plus" you will be able to freely roam the place to gather collectibles. Just don't go to the Lighthouse, where the final battle is. Luckily, there are no collectibles there.

In Arkham Origins Blackgate, New Game+ is unlocked after beating the game once on any difficulty. You might ask, is there a reason to do NG+ in this game, as there are no achievements for finishing the game on NG+? While there are no achievements for finishing NG+, in order to unlock these two achievements you must finish the game at least 3 times, each saving a different boss for last. Each boss will drop the final piece of suit needed for these achievements
Other than that, there's 3 other achievements that requires a unique playthrough each time. Near the end of the game, the final boss you defeated will have one last "surprise" for you. To unlock each achievement, save the corresponding boss for last and the mission will appear.

As someone who just finished one playthrough, you might wonder, what carries over? Here, I will make a list. Know that unlike other Arkham games, NG and NG+ does not occupy different slots, therefore if you do NG+ your story progress will be gone.

• Detective Cases. These easy-to-miss items carry over, so you don't have to scan all items in one run. They unlock bonus readable stories and concept arts.
  
• Batsuit pieces. If you collect all of the available ones in one run, you won't have to find them again. It is recommended that you find the Blackest Night Batsuit, as it's the only one you can fully unlock no matter which boss is last. There's also an achievement tied to it.
  
• Extras. Concept art and movies unlocked will always be available to view from the menu.

In short, only the extras and suits carry over.

As with Arkham Origins, gadgets must be re-acquired due to acquiring them being part of the story. However, when you reacquire a gadget in Origins all upgrades you have unlocked will instantly be unlocked as well. Sadly, that is not the case with Blackgate.

• Gadgets. All gadgets have to be re-acquired. You will start NG+ with a basic Batarang, like in new game.
  
• Gadget upgrades. During the course of the game, you will find some "Tier 2" upgrades for your gear, such as the electric upgrade for the Batarang and tightrope for the Line Launcher. These must be re-acquired to progress the story.
  
• Armor upgrades. These upgrades add your maximum health, and there's a total 8 of them.
  
• Heavy Gauntlet upgrades. These upgrades add more damage to your attacks, there's only 3 of them.
  
• RUSH upgrades. These upgrades add more damage to your attacks as long as you're not taking damage. There's only 3 of them.
  
• Destroyable items. I don't think these items unlock any extras or upgrades, but there are achievements tied to destroying all of each type in one run. There are 20 Joker teeth, 20 Black Mask masks, and 20 Penguin bird cages.
  
• Crypto keys. Basically upgrades for the Crypto Sequencer, allowing you to hack different panels in the prison. These are acquired as part of the story.

In short, all gears and upgrades must be re-acquired every new run. If you're going for The Collector achievement, make sure to collect all upgrades in your final run. And of course collect all suits and cases.

So if you want to get all achievements in Blackgate, you have to do a minimal of 3 runs, while collecting all upgrades in your final run. You don't have to find all Detective Cases and Batsuit pieces in one run, as their progress carry over playthroughs. However, collecting them early will make subsequent runs easier, and you can just focus on finishing the story.

Honestly, I don't like the fact that ALL upgrades must be re-acquired on every playthrough. I have no problem with re-acquiring gears and crypto keys, as finding them feels like part of the story. Same with Arkham Origins, I don't mind having to find the gears all over again. However, there's really no reason to make armor, gauntlet, and RUSH upgrades disappear after every playthrough. Those upgrades are not even connected to the story! They just make your Batman stronger.

As with gear upgrades, finding them does give a bit extra for the story. However, on your second or more runs it gets annoying. Backtracking through the map feels very tedious, and you'll get lost easily. Would be better if upgrades do not need to be reacquired. It would make the story shorter, yes, but Blackgate is too long and tedious for a game we must play at least 3 times from start to finish.

However, I do think that Batman: Arkham Origins Blackgate is still a pretty decent Batman Arkham game, and not one poorly made. It's fully voiced, with voice actors from previous entries reprising their roles.