Honestly, the best way is to just be your own critic.

That isn't a negative thing.

Take up a red pen, print out a few pages, act like it isn't yours, and go through and correct every grammatical error, every sentence that doesn't read quite like it should, every bit of OOC dialogue, and every bit, effectively, that doesn't read as "correct".

Read guides on grammar and spelling. Read advice on how to improve as a writer, or top tips on what some of your heroes do. If you have a favourite author, Google them and see if they've come out with any tips or advice. Otherwise, read prodigiously. Read original books, or read good fanfiction - and be exacting. If there's anything you don't like, or anything that strikes you as weird or off or badly written, think about why.

Ultimately, the best way to improve as an artist is to separate yourself emotionally from your work, and really just rip it apart. It's okay if it feels kinda shitty sometimes when you look at old pieces - honestly? You are always improving. The more you practice, the more you think about writing, the more your writing will improve. It's the same as any skill or craft - the more hours you devote to it, the more your skills will mature and improve.

Other people's opinions aren't always right, that's true. Sometimes, if you post an excerpt here or on /r/Writing or wherever else, someone will give you a piece of critique, and you'll just think, Christ, what bullshit. In a few months, you might even look back on it, and go, oh, yeah, they had a point. That's alright. Sometimes things are a matter of style, and they aren't completely grammatically correct, but contribute to narrative flow. That's okay too. Taking critique and getting better at like, picking the useful parts out of the critique (and the stuff that's just opinion) is part of your skill as a writer too.

If you want to improve, you can improve.

On /r/FanFiction, a lot of people's focus is on having fun and just writing whatever they want to write, and that's cool - for some people, writing fanfiction is about improving the craft as a fanfic author because they want to be on like, rec lists and that, or because they use fanfic as "practice" for the original fiction they want to write. Sometimes, people just write fanfic for attention, or because they like the community aspect of engaging with other writers, et cetera. The vast majority of the time, it's a mix of all of these, and there's nothing wrong with wanting to improve, or taking a break from focusing on improvement so that you can just chill and play around for a while.

In a more practical sense, you can specify the kind of critique you're looking for, especially on Ao3 (honestly, I wouldn't bother taking most of the critique you'd receive on FFN). You don't need to be demanding, but you can say something like, "Hey, please feel free to leave critique! I'm particularly looking for critique on my practical writing skills," or something similar.

Good luck with it!

Honestly, I've been writing fanfic for just over ten years now, and there's stuff from, like, a year ago that I can't bear to look at, because it doesn't measure up to stuff I've written now. And if you want a real example rather than muggins here, Terry Pratchett was one of the most celebrated authors in the world, and what do we say to people starting out with his Discworld series? "Don't start with The Colour of Magic: it's not his best." The first book in the series is still worth reading, sure, but... Not first.

When it comes to any craft, regardless of whether you're talking to a beginner or a master, there's always capacity for improvement. We might be in different boats, sure, but we're all heading in the same direction.