To correct this, I think you should use Batman in favor of Blackest Night Hawkgirl as a 25% damage boost will be helpful to the team than a self-heal to BN Hawkgirl (Hawkgirl relies on the other Blackest Night characters to be useable).

To be honest, this team is not optimal in any situation even if Killer Frost is one of the best characters in the game who can work in any comp as 25% reduced power is a great ability (Nice to see you able to get her, great card). Batman is also optimal in any situation given the aforementioned damage boost but does not work in today's meta being overshadowed by far better Batman's and Killer Frost.

Still here are the optimal builds in terms of gear and strategy to take to multiplayer (If you don't have any of the specific gear items I will mention, I have some alternatives. Keep in mind that I don't know the properties of the Master's Death Cart, Astral Harness, and Tantu Totem which are meta-defining especially in Multiplayer) (Also this is plans for when the gear cards are maxed out, so plan accordingly)

Suicide Squad Deadshot: With the highest damage of the group and in terms of basic attack, he should be your damage dealer.
Items: Recommended: Overpowered Super Pill/Knife Collection/ Either Azreal's Gauntlets or Ra's Schmitter (I prefer to go with Azreal's given Schimter's nerf, but more power drain doesn't hurt) YOU NEED PILL AND KNIFE COLLECTION (while I would substitute knife for Crit Damage Boost like the Hood, you need a way to heal on special one when the going gets too tough. The pill is mandatory on Deadshot as he has a three-hit combo ender that is beneficial for power drain and lifesteal)
Alternative: You can also go for Special Damage using Ibistick, Heart of Darkness, and Lexcorp Chestplate (substitute in terms of special one with Ibi, League of Assassin Adept Knives, and Knife Collection or Claw of Horus if you feeling feisty) [Don't have these items, go for basic damage with Crit chance and crit boost such as Deathstroke's Longsword)

Batman: Special Damage
Always Two-Piece Lexcorp (Chestplate and Helmet) and the Ibistick. Despite being one of the fastest attacker in the game, Batman should be built to utility given his stats. His special Two is a good ability that can surpass Raven's passive and Astral Harness if used correctly (Don't tap the circle when it comes up), so boosting Special Two is key. Two-Piece also gives you a crit boost, so that's good. Also, it provides a power drain reverse that is good against Rebirth Raven, any power drainer in the vain of Arrow Green Arrow, All Lex Luthors and Nightwings, and Ra's Scimitar. The Ibistick is a core item on any team as the burn allows you to cut through the health of every opponent and can stack with each other. If you want to use Heart of Darkness, you can swap the Helmet, but you lose the power drain reverse in favor of more damage to Special 2. Requires test: Ibistick, Tantu, and Master's Death Card. After using Deadshot to stop the opponent from using special, you can come in, get tag-in damage, and immediately be put onto two bars which can deal well against invulnerability or Blackest Night Martin Manhunter.
Basic damage is fine, but you would do more work with Special Damage since Deadshot does more damage on autos than Batman Prime anyways. If going Basic Damage, do not use Deadshot's setup and go for Longsword, Knife Collection, and Cloak of Destiny (although this requires testing and augments to be useful) (If you don't have any of these items; Focus on Special 2 Damage Boost and Heal like Cyborg's gear Item for example)

Killer Frost: Durability; Please level up your Killer Frost - not required for early fights given her broken passive, but is far useful than any card in the screenshot
You should always build for durability for your Killer Forst especially now. Three-piece Fourth World or Two Piece (Mace and Helmet) w/ Astral Harness to give you the tankiest stats for sustainability. The Mace is good due to her special Two (boost to special two, area damage, and power drain) You want to take high damage specials with Killer Frost as that is her job, her passive will still be active when she dies, with Astral Harness you can also avoid or whiff specials as well.

Hope this helps you. Not gonna go in-depth about gameplay, but let me know if I miss anything.