6 months if u study chess 1 hour daily and play 1 hour daily that is give 2 hours to chess every day and in 6 months u will achieve your aim
How to improve my rating
"How long should I take for me to reach a rating of 800-900?"
++ If you start blunder checking before moving, you can get to 1500 within a month.
No study required, only mental discipline.
6 months if u study chess 1 hour daily and play 1 hour daily that is give 2 hours to chess every day and in 6 months u will achieve your aim
It also depends on the knowledge retention ability of a player. 3 months should be able to bring him to 500 (but I hope that can be achieved in a shorter time frame), but getting to 800 or 900 will probably require more than six months.
Also, the OP must be able to realise that a "peak" rating does not represent an average rating, so hitting a rating of 800 during a single game before returning to 700 afterwards does not make him "800 rated". In practice, the OP will experience a series of swings in rating values in almost every rating stage.

6 months if u study chess 1 hour daily and play 1 hour daily that is give 2 hours to chess every day and in 6 months u will achieve your aim
How do I study chess?

I recently began chess around a month ago. I play chess for around about 2 hours everyday
and I feel like I am improving but my rating is stuck between the 200-300 bracket. How long should I take for me to reach a rating of 800-900?
With lots of practice and playing/study, you can reach 1000+ chess.com rating with little more than the fundamentals. This is NOT to say it is easy and comes without work though. It might even take a few months for some people.
What "fundamentals" then? Things like chess opening principles
https://www.chess.com/blog/KeSetoKaiba/opening-principles-again out of the opening stage of the game; for the middlegame, you can practice lots of chess puzzles like the chess.com daily puzzle https://www.chess.com/daily-chess-puzzle and for the endgame stage you can learn the basic checkmates and theoretical endgames. These are endings like Queen + King vs King checkmate or how to use King Opposition to win a pawn endgame with extra material.
My YouTube channel specializes in things useful for the beginner to intermediate chess player, so check it out if you are interested
https://www.youtube.com/@kesetokaiba6161
I recently began chess around a month ago. I play chess for around about 2 hours everyday
and I feel like I am improving but my rating is stuck between the 200-300 bracket. How long should I take for me to reach a rating of 800-900?