This is VERY MUCH a work in progress but I will continue to update THIS post as more are discovered. You can share your own findings as well and I will paste them into THIS post.
ATROCITUS
- Pillar of Blood (cost 1 slot)
Summons forth a pillar of blood and rage. Meter burning adds a second blast (launcher).
- Blood Push (cost 2 slots, credit to pock3tmonstr)
A powerful shot of pure rage blasts the opponent back. Meter Burning increases range and power.
Replaces Napalm Vomit.
Requires both Ability Slots.
- Regurgitate Rage (cost 1 slot, credit to ArgyleReptile)
Dex-Starr rushes forward and vomits rage, causing damage over time.
Replaces Dex-Starr's Blood Ball.
- Siphon Power (cost 1 slot, credit to ArgyleReptile)
Atrocitus drains the power from his opponent, depleting their Super Meter.
Replaces Life Drain
BATMAN *credit to Pan1cMode from TYM*
- Advanced Parry (cost 1 slot)
Allows cape counter/cape parry to be MB
- Bat strike (cost 2 slots)
Replaces Character trait. Summons mechanical Wayne Tech bats that attach to the opponent and explode.
- Boomerang Belt (cost 1 slot)
Replaces MB up batarang. The MB Up batarang now returns to strike an opponent in the back instead of exploding.
- Taser-rangs (cost 2 slot)
Replaces MB baatarangs. All MB batarangs explode in a burst of electricity, stunning the opponents
- Dual Batarangs (cost 1 slot)
Replaces Batarang. Batman flings two batarangs straight ahead.
- Air-to-air Batarangs (cost 1 slot)
Replaces Scatter Bombs. Batman flings a single batarang ahead while airborne.
- Air-to-Ground Batarangs (cost 1 slot)
Replaces Scatter Bombs. Batman flings a single batarang downward at an angle while airborne.
- Evading Bat (cost 1 slot)
Batman rolls backwards from a wakeup and attacks with an evasive manoeuvre
- Cape Parry (cost 1 slot)
Replaces cape counter. Gives batman multi-hitting cape parry (like Injustice 1)
BLACK CANARY
- Body Bounce (cost 1 slot, credit to Ryce)
Meter Burning the Hard Lock attack now bounces the opponent for a combo.
- Air Canary Cry (cost 1 slot, credit to Felix)
Black Canary can use her Canary Cry while airborne.
- Rising Kick (cost 1 slot, credit to Felix)
Gain a vertical kick. Meter Burning follows up with a second airborne kick that launches the opponent up in the air for a combo.
- Sonic Burst (cost 2 Slots, credit to ArgyleReptile)
Black Canary lobs a Sonic Grenade that disables her opponent for a short time.
Replaces Canary Cry
- Clutch Crush (cost 2 slots, credit to 2n2)
Grants Black Canary a powerful command grab in addition to her Canary Cry
BLUE BEETLE
- Mandible Flurry (cost 1 slot)
Blue Beetle extends his back claws and spins, striking twice. MB adds additional launching hit.
- Aculeus Strike (cost 1 slot)
Back claws attack rapidly in a flurry of 5 strikes.
- Crawling Burst (cost 2 slots)
Replaces energy cannon, launches a slow moving projectile and MB increases size and damage. (Editor's note: this move is straight dildos).
SUPERGIRL
- Suncharge (cost 1 slot/disables lasers)
Grants the ability to charge her body with power, reducing damage taken from attacks.
- Kryptonian Grinder (cost 1 slot, credit to Felix)
The Kryptonian Force Meter Burn is replaced with a grab that grinds the victim a great distance across the ground. (Replaces Kryptonian Force Meter Burn)
- Speeding Bullet (cost 1 slot, credit to ArgyleReptile)
Supergirl flies straight ahead while airborne, delivering a powerful punch.
- Earthshatter (cost 1 Slot, credit to ArgyleReptile)
Replaces the limited flight of the Sun Strike Meter Burn with a powerful ground pound attack.
SUPERMAN
- Air Heat Zap (cost 1 slot)
Superman gains a straight, focused blast of heat vision while airborne.
- Empowered Heat Zap (cost 1 slot)
Superman's Heat Zap can now be MB to increase damage and size.
- Krypton Charge (cost 1 slot, credit to Slaythe)
With extreme speed, Superman delivers a powerful flying attack.
- Ground Tremor (cost 1 slot, replaces air flying smash, credit to Slaythe)
Superman smashes the ground with his fist, creating a shockwave of damage. Meterburning adds an additional strike.
- Meteor Drop (cost 2 slots, replaces Supermove, credit to Ryce)
Superman flies into orbit, grabs a meteor, and smashes it onto the head of the opponent, triggering his Supermove.
GEAR SETS
ATROCIOUS
Traitor's Garb (credit to ArgyleReptile)
Set Bonus
[4/4] Force of Hate: 200% increased damage against Green Lantern Corps members (!)
The Five Inversions (credit to pock3tmonstr)
Set Bonus
[2/5] Interaction Boost: Increases Environmental Interaction damage by 10.00%.
[4/5] Heavy Throw: Increases Thrown Environmental Interaction damage by 10.00%
[5/5] Transition Boost: Increases Stage Transition damage by 20.00%.
BATMAN
Plastisteel Tactical Gear (credit to pock3tmonstr)
Set Bonus
[2/3] Bonus Defense: Gain an additional 100 Defense.
[3/3] Bonus Defense: Gain an additional 200 Defense.
[3/3] Kryptonian Defense System: Reduces damage from Kryptonians by 50.00% (Single Player Only).
Insurgent Armor (credit to pock3tmonstr)
Set Bonus
[2/4] Bonus Strength: Gain an additional 100 Strength.
[4/4] Bonus Ability: Gain an additional 100 Ability Power.
[4/4] Arkham Lockdown: 100.00% extra damage to classic Batman foes (Single Player Only).
Kryptonite Infused Armor (credit to ArgyleReptile)
Set Bonus
[5/5] Advanced Swarm: Increased Range on Bat Swarm Power
Billionare's Suit (credit to ArgyleReptile)
Set Bonus
[5/5] Affluent: Increases all currency gained by 15%
[5/5] Billionaire Batarangs: Activates Golden Batarangs
Blue Beetle credit to pock3tmonstr
The Reach
Set Bonus
[3/5] Interaction Boost: Increases Environmental Interaction damage by 25.00%.
[3/5] Heavy Throw: Increase Thrown Environmental Interaction damage by 50.00%.
[5/5] Fury of the Scarab: For every 25.00% of Super Meter above 25.00%, Blue Beetle gains 5.00% increases damage.
Kha-Ef-Re's Regalia
Set Bonus
[2/4] Environmental Resistance: Reduces damage taken from Environmental Interactions by 25.00%.
[3/4] Transition Resistance: Reduces damage taken from Stage Transitions by 50.00%.
[4/4] Heroic Force: 100.00% extra damage to Villains (Single Player Only).
SUPERMAN
Armor of the Yellow Sun
Set Bonus:
2/2 Quick Charge
Superman's Unchained Character Power
Cooldown is reduced by 20%
The House of El
Set Bonus:
2/3 Gain an additional 100 Health
2/3 Gain an additional 100 Defense
3/3 Activates Blue Heat Vision
Regime Regalia (credit to Slayte)
Set Bonus:
2/4 +200 Strength
4/4 Rage: +10% damage -10% defense
Last Son of Krypton (credit to pock3tmonstr)
Set Bonus
[3/5] Heroic Force: 100% extra damage to Villains (Single Player Only)
[5/5] Damage Shield: 10.00% chance to gain a Shield that reduces damage by 50.00% when hit
SUPERGIRL
Alura's Guardian (credit to ArgyleReptile)
[3/5] Bonus Health: +150
[3/5] Bonus Defense: Defense +300
[5/5] Hangtime: Super Hover last 2 more seconds.
Sunlight Armor (credit to pock3tmonstr)
Set Bonus
[4/4] Yellow Sun: Supergirl starts the match with one bar of Super Meter.
There's a megapost somewhere here that has details of the custom moves and gear sets we discovered, including their set bonuses.
. I did a majority of that on mobile so imagine my tenacity there 
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