As an A-/A/A+ player, I'd like to get up to S aswell.
Firstly, learn new weapons, and their strengths and weaknesses. Get outranged by an N-ZAP whilst you're playing as Aerospray? Try outranging your opponents when you next use N-ZAP. If you can work out how to counter a player, then keep trying to do it, maybe in Turf War where there's nothing at stake.
Secondly, notice the gear combinations of those who kill you. If they're using a weapon you'd like to use or already use, maybe there's something in their gear setup that allows them a better chance at the kill.
Also, if your team isn't going for the objective, then YOU go for it, instead of hoping that they'll get it for you. More often then not, you'll just lose the objective to the other team.
Do you die a lot? If so, try thinking about how you could have played differently. Jumped into the centre section on Moray only to be splatted by the Rainmaker shield? Probably a good idea not to jump down there next time. In the meantime, the Quick Respawn ability is your best friend.
Assign gear to a weapon, not a weapon to gear. If there's a weapon you like, think about how you play with it. Running out of ink too much? Get some Ink Saver (Main). Like your special weapon a lot? How's about some Special Charge Up, or, if you die a lot, some Special Saver wouldn't hurt.
One final thing, instead of blaming your team for playing badly, sometimes we need to consider how we could maybe help. Making use of callouts is quite helpful, such as a "Nice" or "Booyah!" when your teammates get the tower, or a "To me!" or "C'mon!" to get them to follow you. Screaming at the TV isn't an option.
Hopefully, I've given you some hints here, from my limited knowledge. These are just some things I've learnt over the course of getting to S Rank.
Not that there's much good about S Rank anyway, besides maybe bragging rights and the ability to squad without worrying about deranking.