Hakumen is very easy to pick up and become decent with, but taking it to the next level is really hard.
IE: Other than Haku-men's j.2c loop, he doesn't have any combo that's hard to learn or execute. (So far)
But to become really good with Haku-men, you need to step your basics up. Things like instant blocking and spacing/footsies become extremely important to Haku-men because he doesn't have the standard bullshit that the other characters have (Though I'm sure Carl players think losing 5k life in one 5 hit combo is also bullshit... )
Being a top level Haku-men means never missing an opportunity to deal damage. If you land a hit, you automatically go into the most damaging combo you can with the magatama you have. Haku-men, against the top three, doesn't get many chances to actually land a hit so you need to make sure you can make those hits count. Haku-men only has a few combos, but he has a lot more ways to get into those combos (6a, 6b, j.c, c, a, 2a, 2b, counters, throws, any of his specials). Regardless of how the combo starts though, most the time you want to somehow get it to end with falling j.c, 2c, sjc j.2c, j.2c, air dash forward, j.2c, j.2c, j.2c (in a corner. Half screen you do j.2c, air dash forward j.c)
Being a top level Haku-men means you IB stupid supers like Noel's or V-13's. Those supers can almost max out your meter by just jumping, holding back for the first hit, and then tapping back to IB the rest (You could try to j.c them, but why risk it?)
Being a top level Haku-men means you IB guard strings. If you see your opponent using the same guard string over and over, you need to be able to IB the 2nd to last hit and counter the last hit. You need to be able to let them know you are going to punish them every time they try to pressure you when you're blocking.
There's probably other things I'm forgetting, but you really need to spend time in training mode getting your combos down, and then spend time in matches so that you can learn to hit confirm them and land them in real matches.
Remember, Haku-men really only matches up badly vs Arakune, Rachel, and v-13. You should respect Ragna, Noel, and Jin but definitely not fear them. And even v-13 gets easier when you play her a million times. She doesn't have THAT much variation on her shit, so learn to block her strings and slowly force your way in. Hope this helps!
If you want to consistently beat Carl, you could always just go to the Carl thread and find out who his worst match up is, and main THAT dude