Here’s; according to the artist, the list of special moves, fatalities and friendships for the characters:
 
TWILIGHT SPARKLE  
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Special moves:
Teleport Kick - Twilight appears right before her opponent and kicks it away.
Magic Ball - Sends an orb of magical energy at the opponent.
Telekinetic Slam - Lifts opponent into the air and forcefully drops afterwards.
Counter - Parries opponent’s attack by teleporting behind it and kicking it away.

Fatality 1: Piercing Horn - Twilight pierces opponent’s chest with her horn, then proceeds to channel magical energy through opponent’s body, causing it to explode.
Fatality 2: Magic Overflow - Twilight taps into her limitless magic potential, ripping her opponent to shreds in a bright flash of light.
Friendship: Writes a letter to Princess Celestia.

APPLEJACK
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Special moves:
Apple Toss - Applejack kicks an apple toward the opponent.
Power Buck - Kick with her hind legs, sending opponent at the edge of the screen.
Lasso Grab - Attempts to grab opponent with a lasso and lure it to Applejack for a free hit.
Tasty! - Eats an apple, restoring 5% of health bar.

Fatality 1: Hard Landing - Applejack smashes her opponent into the air with immense strength. The force of impact instantly breaks opponent’s neck.
Fatality 2: Stampede! - Applejack calls Winona and they lead a cow stampede that makes quick work out of opponent.
Friendship: Does several tricks with her lasso.

DERPY
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Special moves:
Stun Bubble - Derpy sends a burst of bubbles at the opponent. If unblocked, bubbles paralyze opponent briefly.
Torpedo - Flies toward opponent at high speed, crashing onto it.
Mail Box - Slams opponent with a mail box.
Muffin Bomb - Throws an explosive muffin at the opponent.

Fatality 1: Cross Trick - Derpy approaches opponent, looking at it with cross-eyes. A moment later, she grabs opponent by the mane and removes the head from the body.
Fatality 2: Happy Landings - Derpy lifts her opponent into the air and drops it to the hard ground. With broken legs, the victim lays down, as Derpy falls on opponent’s back.
Friendship: Turns toward the screen, says: “Muffin!” and smiles.

ZECORA
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Special moves:  
Trance - Forces opponent to approach Zecora. Allows free hit.  
Potion Bang - Tosses an explosive vial at the opponent.  
Spirit Swing - Swings a mask at the opponent, launching it into the air.
 
Fatality 1: Penetrator - Zecora draws a spear and uses it to penetrate opponent’s body.  
Fatality 2: Ancestral Curse - Zecora performs a chant that casts a curse on the opponent. It then breaks its own neck.  
Friendship: Balances on her bamboo pole.
 
 
COLGATE  
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Special moves:
Cold Breath - Freezes opponent in place with an arctic breath. Works only on close range.
Brush-Off - Slides toward opponent to trip it.
Ice Clone - Creates a freeze-on-contact clone.

Fatality 1: Shatter - Colgate chills her opponent to bones and breaks it to pieces with a single kick.
Fatality 2: Slippery Pop - Colgate freezes her opponent, takes it on her horn and attempts to balance it, but the frozen body drops to the floor and breaks. Colgate shrugs.
Friendship: Makes a toothbrush clean her mane.

TRIXIE
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Special moves:
Flying Sparks - Can summon up to three sparking balls to be fired at the opponent.
Morph - Briefly transforms into Trixie’s opponent, receiving its entire move set.

Fatality 1: Soul Steal - Trixie impales her opponent on her horn and lifts it up, draining its soul, accompanied by an evil laugh. She then drops the lifeless body to the ground.
Fatality 2: Thunder Cloud - Trixie calls a huge dark cloud over her opponent’s head. The vicitim is later struck down by a powerful lightning and burned to ashes.
Friendship: Sets off a few fireworks and poses.

RARITY
 
Special moves:  
Horn Charge - Rarity slams her horn into opponent, sending it away.  
Scream - High pitched scream that briefly stunts the opponent.  
Pillow Barrage - Magically sends pillows at the opponent.  
Reflect - Reflects opponent’s projectile attacks.
 
Fatality 1: Diamond Storm - Rarity conjures up several razor-sharp crystals and sends them toward the opponent. The crystals slice through opponent’s body, leaving it torn to pieces.  
Fatality 2: Dress to Kill - Rarity twirls a dress around opponent’s neck and squeezes it to point the victim dies of suffocation.  
Friendship: Grabs the camera and makes “big, cute eyes”.
 
 
BIG MACINTOSH  
 
Special moves:  
Power Buck - Big Macintosh kicks opponent with his hind legs. It bounces of the wall, allowing another hit if Big Macintosh is close enough (but not uppercut).  
Quad Slam - Throws the opponent four times. Works only on close range.  
Shake - Stomps the ground, dealing damage.
 
Fatality 1: Megaton Buck - Big Macintosh hits his opponent so hard that his legs pierce through it, as the victim dies of bleeding.  
Fatality 2: Arm Ripper - Big Macintosh forcefully removes his opponent’s front legs from the rest of its body.  
Friendship: Plays with Smartypants.
 
 
PINKIE PIE  
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Special moves:  
Gift - Pinkie tosses a gift on the ground - it explodes, dealing damage to opponent if close enough.  
Balloon Shield - Negates opponent’s projectile attacks.  
Frame Out - Exits the screen frame and appears behind the opponent.
 
Fatality 1: Pinkie Sense - Pinkie’s tail starts twitching rapidly, resulting in a flower pot, an anvil, a hay car and a piano to drop on the opponent.  
Fatality 2: Portal Drop - Pinkie creates a portal of void below her opponent and sends it through it. The victim reappears as a skeleton.  
Friendship: Dresses up in her ridiculous costume from “Dragonshy”.
 
 
VINYL SCRATCH  
 
Special moves:  
Razor Disc - Throws a CD at the opponent. Can be controlled.  
Rhytmic Beat - Deals a 3-hit combo. Works only if the intial hit connects.
 
Fatality 1: Party Hard - Vinyl Scratch drops a jukebox on the opponent.  
Fatality 2: Neon Light - Vinyl directs a burning neon light at the opponent, incinerating it.  
Friendship: Brings out a DJ turntable and plays some music.
 
 
FLUTTERSHY  

Special moves:
Vine Whip - Fluttershy whips a vine at her opponent, trying to grab it. If successful, opponent is lured in for a free hit.
Butterfly Swarm - Sends a swarm of butterflies at the opponent.
Takedown - Flies toward the opponent it attempt to grab it and slam it to the ground.

Fatality 1: The Stare - Fluttershy stares into opponent’s eyes, paralyzing it. A few moments later, she calls her animal friends to wail at the opponent.
Fatality 2: Flutterage - Fluttershy turns furious, yells: “You’re… going to LOVE ME!!!”, grabs opponent by the mane and shakes it violently, until the head is removed from the body. She then spits the head away, calms down and stares innocently at the screen.
Friendship: Takes a deep breath and says: “Yaay.”

RAINBOW DASH
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Special moves:  
Rainbow Flash - Rainbow Dash fires rainbow-colored ring projectile at her opponent.  
Air Drop - Used in air. Instantly drops at the opponent, dealing damage on contact.  
Crash Into Hello - Flies toward opponent at high speed, dealing damage on contact.  
Spin Cycle - Spins around, launching opponent into the air if its close enough.
 
Fatality 1: Sonic Rainboom - Rainbow flies from the sky at sonic speed, zipping right past the opponent. The intense speed removes whole skin from the opponent, leaving only a bare skeleteon.  
Fatality 2: Light-speed Beatdown - Rainbow Dash beats her opponent down, ending the finisher with knocking the opponent into the air and allowing it to crash.  
Friendship: Makes a rainbow appear over her head.