You're definitely lacking matchup exp vs PacMan. The biggest mistake is how you rush-down into the hydrant setups. PacMan's "run-off -> FSmash" hydrant launch breaks your particular approach angle.
Throughout the video, you're pretty much attacking where PacMan is at the moment. You need to aim and attack where PacMan
will be: roughly one fox-trot behind the Hydrant. Never attack Pacman's "strong zone" area, you need to avoid that area at all costs. And certainly don't attack the Hydrant when Pacman is close: the Hydrant has hit-stop penalties (your character slightly freezes when it attacks the Hydrant).
That's my opinion anyway, from these matches:
https://www.youtube.com/watch?v=P-Qu8J9dIaQ
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PacMan also freezes when he attacks the Hydrant, but the PacMan player will generally have more experience than you on that subject. In either case, if you see a FSmash or some other big attack on the Hydrant, you will generally have an opportunity to rush in afterwards.
In effect, your timing for your rushdown is poor. You're attacking precisely when PacMan is strongest. If you delay slightly earlier or later, you'll have an easier time. Alternatively, you need to come in from an angle where PacMan's weaker. Jumping in from a higher angle will force PacMan to move around more, because PacMan doesn't have very many options to stop a high-angle approach (Ex: Bayonetta / Greninja angles). Inkling can get there with maybe a double jump, or an aerial Side-B.
With a bit more experience, you'll recognize the launch angles of certain Hydrant setups. Ex: Hydrant -> FSmash. Typically, you can run-under the Hydrant (especially a small, fast character like Inkling). Of course, the opponent can change the launch angle at will by choosing different attack, but the various attacks (FSmash, FTilt, DTilt, and BAir) all launch the hydrant at a similar angle that Inkling can definitely run under afterwards.
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There were times when you could have gimped PacMan. If PacMan is very far from the ledge, attack the
POWER PELLET, which breaks his recovery. You had lots of opportunities, but you probably didn't know this fact. Aim at the
POWER PELLET to destroy PacMan's recovery, not PacMan himself. PacMan still will have Trampoline, if you can steal the 3rd jump, PacMan's recovery greatly diminishes. Be careful though: the 4th jump is a guarenteed death, so be sure to time it to jump on the trampoline exactly on the 3rd time.
Failing to Gimp Pacman will result in lots of damage: the Power-pellet move has high-KO power, while the Trampoline can kill you if you mistime your attack. Nonetheless, with a bit of practice, you can consistently gimp PacMan's recovery.
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The PacMan you played against was relatively a rushdown style PacMan. Certainly more aggressive than I would have been. It seemed like he was very good at Galaxian combos, as well as converting a lot of damage off of small hits. But I think he was a bit spammy with his Smash attacks and needed to play more carefully as well.
I'm personally quite passive and defensive though. I prefer not to rushdown unless I have an overwhelming advantage (ex: Melon or Galaxian in play, or Slowly-bouncing Hydrant).