While it is hard to fully judge a set with such few moves, I will nevertheless share my thoughts on this "core".
Also, I'mma be brutally honest here. Brace yourself.
Right off the bat, I'm not a fan of the "cycling bombs" deal on neutral special for a few reasons:
- They cycle, rather than being separate moves. This drastically limits the Inkling's options at any given time; if you need a Splat Bomb, you very well may not get one, so you can't do that effective setup that uses the particular bomb type. It also irks me that you can't actually use the Burst Bombs for their rapid-fire attribute due to this, which is their only real strength. Randomized and cycling moves are never better than a choice between them.
- Inklings shouldn't be focused on bombs, or rather, sub weapons. They're sub weapons in the game for a reason; they're complimentary to main weapons like the shooters, rollers, etc, but not at all the main focus. It's like if Link used the boomerang for the majority of his moveset, rather than his sword. Don't put a complimentary tool on two specials, or even neutral special unless it doesn't fit anywhere else -- these would be perfectly serviceable on down special. (Squid swimming would fit best on a special crouch, I feel.) That said, a bomb-focused Inkling could be an interesting idea, but it needs to be refined, and fleshed out with a full moveset that really takes advantage of the different bomb types.
Moving onto side special, it's really not a very logical place for a charger weapon to be. The idea behind a charger is that you're practically immobilized while charging, and thus vulnerable, but you unleash a powerful attack at the end. On side special, the charger loses that key weakness -- you might not be able to walk during the charge, but aerial momentum in combination with a jump makes that a rather moot point. A smash attack, however, passes that test with flying colors -- heck, you can aim them too. Mega Man shows us that projectile smashes can work just fine. It's just a bit of odd move placement, though, nothing too serious.
(implying that anything pertaining to hypothetical Smash Bros. movesets is particularly "serious" haha)
Up special is mostly fine, although I disagree with the lack of vertical movement, seeing as how in Splatoon, you use it pretty much exclusively for horizontal movement.
Down special is probably my main issue with the set. Everything I said for neutral special applies here as well. First off, this isn't a very good use of ink at all. In Splatoon, ink is used for mobility, and for outmaneuvering opponents. Here, though, there's no indication that you can move at all, or that if you can, it'd be any faster than dashing. Then there's the ammo limit. Ammo limits A) don't add depth, B) add an annoying limitation to distract the player from the actual battling, and C) are a rather cheap excuse to try to "balance" a character. Rather than limiting how many times you can use an attack, instead change the attack itself for a more elegant solution to the balance issues. The idea of laying down traps while swimming in ink is a neat one, I will say, but I don't think that it's really a good main use for ink as you're making it seem like it is.
Multiple final smashes are fine enough, although I'd change how they're activated; blocking usage of up special when you're offstage, for example, wouldn't end too well.
I don't want to come across as too harsh here. While I do disagree with a lot of the decisions here, it's cool to see a different approach to the idea of the Inkling. There's definitely a lot of potential for an Inkling moveset, after all.
(but mine is still the best
)
I'll add this to the OP once I get the chance, by the way.