What should I know? What should I be doing? What should I use? etc
What should you know: A- is rough because, in my experience, there is a big skill difference within the rank itself. There are people who still play like B's and people who play like high A+. It is difficult to carry in this rank because you might play the best in your life and still lose, which is terribly frustrating (I went 17/4 once in TC and still lost as no one else on my team had a positive K/D).
What should I be doing: Like a previous poster said, get good at movement. Swim strafing in firefights, when to rush someone down, how to position when anticipating someone. Also, get good at re-positioning your aim after a swim strafe - this is often the thing that will let you win fights. It means nothing if you can out maneuver them but cant splat them. Get better at map awareness; use your peripheral vision to track people so that you don't get flanked as often. Map awareness also incorporates common paths that people take and trying to cut those paths off. Watch youtube videos and streamers to get a sense of some of these things: what patterns emerge, what are effective strategies, etc.
Keep in mind though, even if you know all these concepts about patterns, positioning, movement, etc, if you don't have solid aim or can't execute, then you will still struggle (this is my life right now). So, the best way to do this is to practice and not give up.
What should I use: First, use what you are comfortable with. You could try picking up the meta weapons (.96 deco, .52 gal, tentatek, etc.) but if you aren't comfortable with them then you won't win. You will have success with a weapon that you know; its limitations and strengths, its range and strategies. That being said, longer range weapons are typically the better performers. The Tentatek/Octoshot and the .52 Gal are generally considered the best jack-of-all trades weapons, and if you haven't already, I'd start with one of those. They are mid-range, but do just about everything. If you want a longer range weapon you could try the .96 deco, the forge pro, or the dual squelcher. The trick with these longer range weapons is to really use their range as you might be in trouble if people close in on you. The advantage is that you can often just sit back and splat people or push the objective from afar.
Good luck!