Run animation: this is the normal run from the original games, not the Talon Trot. Banjo is the one who walks.
Neutral Jab: Claw Swipe. The normal jab from Banjo-Kazooie, with Banjo swiping his claws forward three times.
Neutral Jab (Infinite): Claw Swipe + Peck. It begins as Banjo-Kazooie's jab, then it transitions into Banjo-Tooie's jab, with Kazooie pecking forward. The final hit could be a wing swipe, or Banjo clawing again, or something like that.
Forward Tilt: Beak Bayonet. The move you did in Tooie when you pressed B while in Breegull Blaster mode. Banjo takes Kazooie out of the backpack, and he swings her forward like a bayonet. It has a lot of range and can KO.
Up Tilt: Peck. The jab from Banjo-Tooie, again, this time executed while Kazooie is pointing upwards.
Down Tilt: Wing Wack. A heavily reworked version of Kazooie's solo attack. Banjo crouches, Kazooie extends from the backpack and swings her wings forward multiple times.
Dash Attack: Roll. Banjo rolls forward, with Kazooie's wings sticking out, just like in Banjo-Tooie.
Forward Smash: Breegull Bash. Of course, the forward smash has to be this secret move from Tooie. Banjo takes Kazooie out and slams her violently to the ground in front of himself. This'd be their best KO move. Complete with "Breeee-booown..." "GYAH-HUH"
Up Smash: Shock Spring Jump. This is the move that Banjo & Kazooie did when they pressed A on a Shock Pad. The move is pretty slow, during the charging fase Kazooie brings her legs out and concentrates her strenght on the ground. Then, the duo springs very high in the air, while Banjo claws/Kazooie swipes her wings. This up smash is unique, in which your character jumps very high. Like, if you do it on the center on Battlefield, when the move is finished you'll land on top of the central platform. The range is silimar to that of Palutena's up smash, though.
Down Smash: Beak Barge. The Z+B move in both Kazooie and Tooie. Banjo ducks, then he propels forward with Kazooie extending her beak in front of herself. It'd work kinda like Megaman or Cloud's down tilt, but it is a smash attack, so it can be charged and it is pretty powerful. The duo propels forward, but the downside is that the move doesn't hit behind them.
Grab: Taxi Pack. Banjo's solo special move from Banjo-Tooie. The pack magically expands, Banjo swings forward with a motion reminiscent of the one Villager does when he uses his net, just that it goes down-up instead of up-down. Kazooie still stays inside the backpack.
Pummel: Kazooie, while still inside the backpack, pecks on the duo's victim's face.
Forward Throw: Grip Grab. Kazooie slouches a bit, then she hits the opponent 3 times with the same animation she did when you pressed B while grabbing a ledge in Tooie. The third hit launches the opponent away. I envision it as a combo throw.
Up Throw: Shack Pack + Wing Whack. Kazooie hops off the backpack, while Banjo closes the opponent inside it and launches him upwards a bit. The shape of the backpack now is just like the one it had in Tooie when you used Shack Pack as solo Banjo. Kazooie hits the backpack with her wings 3 times, then the opponent comes out and gets launched away.
Back Throw: Stilt Stride. Banjo grabs the opponent with his hands and puts him behind him. Then, Kazooie extends her legs out of the backpack while wearing her boots, and kicks the opponent away.
Down Throw: Sack Pack. Banjo jumps in the air, while Kazooie slams the opponent to the ground. Banjo hops inside the backpack together with Kazooie, and they slam onto the opponent. They jump again and they return to their idle pose. This is a reference from one of Banjo's solo moves in Tooie. This is their KO throw.
Jump: Banjo jumps in the air, with the same animation he had in Kazooie and Tooie.
Double Jump: Feathery Flap. Kazooie sticks out of the backpack and propels the duo upwards with her wings, again, just like in Kazooie and Tooie. Comes packaged with the obligatory "aww-breeeeeee".
Neutral Aerial: Wing Whack. This is the move that Kazooie did in Tooie when pressing B while on her own. Of course, this time it is with Banjo, and the angle of the hits changes a bit. I imagine it to be kinda like Piranha Plant's neutral air, for reference.
Forward Aerial: Rat-a-tat Rap. The iconic aerial attack from both games. Kazooie sticks out of the backpack and pecks in front of herself. The duo's momentum slows down for a bit, just like in the original games.
Up Aerial: Flap Flip. A similar animation to the Z+A move in the original games, just a lot faster, and mid-air. Basically, a backflip with Kazooie's wings extending around the duo. It should have a lot of range.
Back Aerial: Pack Whack. Banjo's solo offensive move in Tooie. It's still pretty similar, but reworked to be a back aerial. Banjo turns around, takes off his pack and he swings it in front of himself. Slow but powerful move.
Down Aerial (Version One): Beak Buster. You tap A and the duo comes falling down, with Kazooie's beak pointing downwards. It works like Sheik, Sonic or Ridley's down air. It has a lot of knockback.
Down Aerial (Version Two): Bill Drill. This variation is activated if you keep A pressed. It's slower and it takes a bit to charge, but Kazooie's beak then acts as a drill, dealing massive damage on anyone it hits. This is from Tooie, of course.
Neutral Special: Breegull Blaster. The FPS move from Tooie. If you tap B, Kazooie shoots a blue egg which travels forward on a straight line. 3 blue eggs at a time can be on screen. If you keep B pressed for a bit, Kazooie shoots a fire egg. It's more powerful, but, of course, slower. If you keep B pressed even longer, Kazooie fires a grenade egg, which deals a lot of damage.
If you tap the stick in the opposite direction after you have pressed B, Kazooie will instead shoot the egg from her derriere. The egg doesn't go in a straight line, but it falls down and it springs for a bit, just like it happened in Banjo-Kazooie when you shot an egg from behind.
Side Special: Talon Trot. The duo starts to run around on Kazooie's feet. The speed is faster then the one in their normal run. They can jump while in this state, gaining a bit more distance then when they jump normally. If you press B again while you're in this state, Banjo will jump off Kazooie and swing his backpack while Kazooie extends her beak. If sweetspotted, it deals a lot of damage. If you don't press B, after a while the duo will lose speed, and Kazooie will retreat inside the backpack. You can't stop while in this form.
Down Special: Wonderwing. Kazooie protects Banjo with her wings. It works kinda like Joker's rebel guard. You take the damage from a hit, but don't suffer the knockback. If you press B at the right moment, it acts as a counter. Unlike rebel guard, though, you can move while in this state, and you don't summon Arsene of course. Useful to move through projectile spam, for example. You take the damage but you close the distance.
Up Special (Phase One): Flap Flip. The Z+A move in both Kazooie and Tooie. Banjo ducks, then he backflips thanks to Kazooie's wings. The duo goes pretty high in the air, but the movement is pretty much only vertical, the horizontal range of the move is very poor.
Up Special (Phase Two): Beak Bomb. While Kazooie's wings are still extended, you can press B again and select a direction, then Kazooie will launch the duo forward. It'd work kinda like Fox's up special, but it'd be a single-hit move, like Ridley's. Kazooie's beak acts like a sweet spot, of course. If the move hits somebody or something, Banjo & Kazooie receive a little bit of recoil damage, just like in the original games. You can also spot a single red feather coming out of Kazooie when they use Beak Bomb.
Final Smash: The Mighty Jinjonator. Banjo and Kazooie grab in front of themselves. If the move connects, a cutscene trigger when the opponent gets slammed on the floor of Gruntilda's Lair's rooftop, while Banjo & Kazooie evoke the Mighty Jinjonator who proceeds to hit the opponent violently multiple times.
I don't know about taunts or victory screen, but there's plenty of animations to grab those from, from both of the games.
I think this wouldn't be well-balanced at all, but I'd like to see something in this spirit, to really highlight the fact that they're a duo fighitng as a singular entity, and to reference the highest possible number of abilities from the original games. After all, Banjo & Kazooie became famous for their vast arsenal of moves and for how wacky some of those could get, I think it'd be great to represent as much of that as possible in their moveset.