✦ Please enjoy the game. If you're not having fun, you shouldn't be forcing yourself to play. This is the most important advice that I can give you.
✦ Generally, you should always strive for 99%+ accuracy on any given map. Anything below 98% should be considered undesired and you need to improve your tapping or rhythm sense. This is more a rule of thumb than anything else.
✦ Try to master alternating as soon as possible since it's essential to increasing your skill cap (full alt is optional).
✦ Stop spamming maps that are way out of your comfort zone. If you're consistently getting anything below an A you should probably be playing easier maps. This does not mean that you should never push yourself, but don't make it a habit. It pains me to see so many beginners with top plays consisting of only B:s and C:s.
✦ Build a solid foundation for all skill sets. Being able to play a wide variety of maps makes the game way more enjoyable. Don't be a one-trick.
✦ You should make it a habit to always submit local scores despite being dissatisfied with them. They serve as a benchmark and are essential to see where your current skill level is and if you're improving. Relevant metrics are accuracy, combo and miss count. Strive to improve all three at the same time, but you should be satisfied if only a single metric is improved.
✦ If your hands are hurting in any way, you should stop playing immediately and take a break. It's important to respect your body's signals. Note: strain and pain are different things.
✦ I recommend finding rivalry in your rank range or skill range. Friendly competition is a fantastic way to push yourself towards improvement. Though, you should be mindful of not letting comparison discourage you because that's not the point.
✦ Mind set is everything. You need to believe in yourself or you're not going to get anywhere. Stay confident no matter what. This famous WhiteCat clip is a perfect showcase of this.
✦ Bad days are NORMAL. There is not a single player out there that plays at their peak constantly so don't be too hard on yourself. Nobody, except maybe yourself, would ever "bully" you for not playing at your best.
✦ Avoid hyper focusing on improving a single skill. Your other skills risk decaying and you could end up in a worse position than before. Make sure to play a wide variety of maps and enjoy the game. Play the songs you enjoy.
✦ Avoid changing your area/sensitivity, skins, cursor size, and so on too frequently since it'll destroy your muscle memory and consequently your consistency. I, myself, have struggled with this many times throughout my osu! career.
✦ This ties a little into my advice about enjoying the game, but remember to never have expectations when you play. Not being able to achieve something because of high standards will be frustrating and demotivating and should therefore be avoided.

That's it for now. You're well on your way to becoming an osu! rhythm champion!