I'm having a hard time thinking of a moveset for Banjo and Kazooie. Not because they don't have enough moves, but because they have so many moves that every input has several viable possibilities and I can't think of the best one for all but a few of them.
Well you are in luck. I just so happened to have come up a Banjo Kazooie moveset back in the Smash 4 days. I have listed everything down and the kitchen sink. This one is going to be long. Please tell me if I have missed anything.
Neutral combo: Banjo swipes with his left claw, then his right claw and Kazooie pops out of the bag and finishes the combo with a peck. It is a 3 hit combo.
Dash Attack: Banjo executes the roll attack from Banjo Kazooie and Kazooie wraps around him like in Banjo Tooie.
Side Tilt: Kazooie pops out of her bag while Banjo crouches over to reach in for a peck attack.
Down Tilt: Kazooie's wings elongate and flaps them together like she is clapping. This attack has a small wind box if the opponent is far enough to just miss the attack.
Up Tilt: Banjo attacks with a headbutt upwards with Kazooie following along with a peck. Banjo headbutts just like Mario's Up smash in Super Smash Bros. N64 that combos into Kazooie's peck attack afterwards
Neutral Aerial: Banjo performs the pack whack in a vertical motion where he flips to attack. Kazooie extends her neck to peck at anyone. Kazooie is the sweet spot and knock back from it depends on which way Kazooie was facing before the hit was done.
Forward Aerial: Banjo bends his head down allowing Kazooie to attack. Kazooie then performs the Rat-a-tat Rap move from Banjo Kazooie that does multiple hits.
Back Aerial: Kazooie slashes both of her wings apart from behind like swords while Banjo looks back to see what Kazooie is doing. This does moderate knock back.
Up Aerial: Banjo and Kazooie perform a pseudo flap flip to kick both of his feet upwards. This has high knock back and is similar to Fox's up aerial.
Down Aerial: Banjo grabs his backpack and swings it downwards while Kazooie pecks her beak. This is a meteor smash.
Forward Smash: Banjo and Kazooie perform the Beak barge ability where Kazooie will lunge forward with Banjo in tow.
Up Smash: Banjo and Kazooie perform the flap flip technique but it is performed like a flipping bicycle kick instead of a jump.
Down Smash: Banjo grabs Kazooie's feet from the backpack and readies his attack. Banjo then performs the Breegul Bash ability where he grabs Kazooie like a club and slams her down onto the floor.
Neutral Special: Egg Firing/Egg aiming - Kazooie fires three normal eggs in a burst shot fashion. Holding down the B button performs Kazooie's egg aim and uses egg grenades instead, allowing Kazooie to aim with a reticle and releasing the button will let Kazooie shoot one egg grenade in the specified direction.
Side Special: Talon Missile - Banjo ducks down and then Kazooie launches herself forward. It is the grounded version of the Talon Torpedo where she will target the closest enemy in sight and give chase. She will return to Banjo once she successfully hits her target or gets hit.
Up Special: Kazooie Flight - Kazooie will take flight inside Banjo's backpack, taking him aflight as well where she will quickly use up all of her feathers in an aesthetic sense and the duo will go into freefall. Similar to Pit's
Down Special: Clockwork Kazooie - Essentially a clone of Bowser Jr's Mecha Koopa. Kazooie coughs out a Clockwork Kazooie egg. It will walk around the stage and explode after 5 seconds. It can be picked up and thrown to explode on contact.
Final Smash: Dino Banjo & Dragon Kazooie - Kazooie flies out from Banjo's bag and is engulfed in a mystery egg that transforms her into Dragon Kazooie where Kazooie dashes across the stage to hit any opponents while Banjo watches. If any opponent is hit by it, they will be brought to the top of the screen where Kazooie circles around and shoots fire and ice eggs at the tumbling opponent(s). Once exausted of the eggs, Dinosaur Banjo will appear and take a large chomp at the helpless opponents. If the opponents are above 100%, it will instantly KO the opponent, otherwise they'll be sent flying. Banjo and Kazooie then return to their normal selves.
Grab and pummel animations: Kazooie exits Banjo's bag as Banjo swings his backpack towards the enemy somewhat similar to the Taxi Pack. The enemy is then trapped in the bag where Kazooie pecks at the enemy.
Forward throw: Banjo kicks the bottom of the backpack which launches the opponent out of the backpack to where Kazooie will return to.
Back throw: Banjo performs a swing similar to the pack whack on the enemy inside until he throws them out of his backpack to where Kazooie will return to.
Up throw: Banjo swings his backpack upwards to where Kazooie pecks the underside of the backpack which will launch the opponent upwards. Kazooie will return to the backpack afterwards.
Down throw: Banjo slams the backpack down and Kazooie performs the bill drill ability where Banjo will clap at Kazooie until the opponent is sent out of the backpack. Kazooie will return to the backpack afterwards.
Entrance animation: A picture frame appears at the start of the match with jiggies placing themselves together to make a Banjo Kazooie painting. Once completed, Banjo and Kazooie will jump out of the painting with it disappearing afterwards.
Crouch/Crawl: Banjo crouches exactly as he does in the games. He cannot crawl.
Idle animation 1: Kazooie pokes out from Banjo's backpack and starts playfully pecking Banjo while he tries to scratch her away. Kazooie laughs and then returns to the backpack.
Idle animation 2: Banjo holds his hand up to his chin while Kazooie shifts from left to right trying to see what's going on from afar. Banjo then puts both hands on his hips and nods while Kazooie returns to the backpack.
Sneaking: Banjo tip-toes like he does in his games.
Walking: Banjo casually walks along as he does in his games.
Running: Banjo and Kazooie side flip around as Kazooie performs the talon trot ability. If Kazooie jumps or stops, Banjo and Kazooie will once again side flip to allow Banjo to stand up or jump.
Item grab idle: Kazooie picks up the item and stays above the backpack at waist level.
Item throw normal: Kazooie throws the item casually as if she is throwing it away.
Item throw smash: Kazooie throws the item with much more force.
Batter Item neutral: Kazooie leans on top of Banjo to hit anyone in front of him.
Batter Item forward tilt: Kazooie swings the battering item forward with Banjo adjusting himself for Kazooie to get the most reach
Batter Item Smash attack: Kazooie swings the battering item with Banjo spinning around to let them item hit the opponent.
Home-run bat Smash: Kazooie cheekily winds up a swing to hit the unaware Banjo. At the apex of her swing, Banjo looks down to see something and Kazooie misses the swing which will hit any opponent in front of them.
Shooting item: Kazooie takes aim with the weapon while Banjo crouches down as if performing the egg firing ability.
Heavy item carry: Banjo lifts up the item with a little struggle and holds it similarly to Mario, except that Kazooie tries to lift it with Banjo.
Hold Assist Trophy/Special Flag/Bomber: Kazooie holds up the item to the sky with an open mouth smile expression as with Banjo who looks up with both fists on his hips. When the special flag has been collected, Banjo jumps slightly upwards as he gives a hi-five to Kazooie.
Sleep: Banjo hops into his Backpack and kicks a sleeping Kazooie out to the top of the backpack. Banjo's head is visible from the top and sleeps in the same position as he does when he sleeps in the intro cutscene of the game. This references the snooze pack ability.
Wake up: Kazooie realises where she is and pecks Banjo to wake up where he swaps places with Kazooie to return to the idle animation.
Up Taunt: Banjo pulls out a Gameboy and plays on it for few seconds as Kazooie watches. Then puts it away to get back up.
Side Taunt: Kazooie sprouts her legs out from the backpack to perform the talon trot, holding Banjo upwards. Kazooie then runs around in a circle making Banjo feel uneasy enough to cover his eyes ending with Kazooie jumping slightly upwards. Banjo then gets on to his feet and Kazooie returns to the backpack.
Down Taunt: Banjo grabs Kazooie out of his backpack, stretches her out in the form of the Breegull blaster ability and faces the camera while looking mean. Banjo then puts Kazooie back in his backpack.
Victory animation 1: Banjo jumps up and waves a jiggy puzzle piece left to right and hands it over to Kazooie who eats it. Similar to how it's done in Banjo Kazooie when Banjo collects a Jiggy piece.
Victory animation 2: Banjo plays on his Banjo while Kazooie plays on her Kazoo and finishes off with Banjo and Kazooie looking at the screen with Banjo's head slightly looking to the right and Kazooie looking to the left. Just like at the end of the opening scene of Banjo Kazooie.
Victory animation 3: Banjo quickly performs a dance and bows in three directions afterwards. Similar to when he collects all the jiggies from a world in Banjo-Kazooie. In team battles, this victory animation will always play when Banjo Kazooie are not the top players.
Losing animation: Banjo stands upright and claps respectfully with a smile while Kazooie is behind Banjo in his backpack glaring into the distance, supposedly at the winner.
Kirby hat: Kirby dons on the top of Banjo's scalp complete with the hair and bear ears. Kirby also wears the backpack for when Kirby performs the Egg fire attack, another Kazooie appears from his backpack.