I'm finding that in Dropshot, your aerial control needs to be good. There is very little applicable use for staying grounded when you could be contesting for ball possession before your opponent touches it. That being said, in situations where you won't be able to hit that air ball before they will, it's crucial to position yourself in a spot where you think they'll shoot it to. But remember to give extra room so you have space to accelerate and hit the ball harder.
I notice some folks forget to let the ball touch the ground at times, and others get panicky when the ball is in their half of the court and start desperately making contact in any way they can.
Today I started letting the ball hit our side deliberately in the interest of being able to get a solid hit on the ball. If the ball isn't charged, I worry less about the damage it does, because heck, until half the floor is gone, we still got room to play, so rather than prioritizing the ball not touching our floor, I'm prioritizing where we will play the ball and how well we can keep striking the ground and maintaining possession. It doesn't matter how often you can keep damaging the floor; in the end, the ball needs to go through it, so if there are openings already, it's best to start pushing the ball in that direction, rather than just kicking it anywhere.
Offensively, there is no sense trying to hit it as many times as you can. If the first objective is to hit the floor, then you should be aiming for areas where there is no one. Teammates who aren't in possession of the ball should look to redirect the shot because a defender will most likely be ready to block. Granted you redirect downward and not upward, towards the wall or corner curve, the shot will more than likely hit the floor.
Otherwise if I can't get a good hit on it when on defense, my next priority is to touch the ball ever so lightly when it's coming to our side so we get possession of the ball and can dribble it around.
Don't stress yourself out with contesting for possession on an uncharged ball. I don't know how many hits you need to get to level 2, but so far I'd say until they... or you get it to that level, let the other players do whatever, and then when you have the opportunity to push a level 2 or 3 ball somewhere, do it. Hitting an uncharged ball around may not be a good idea either. It's kind of like Hot Potato where if you're the last person to hit it until it goes into a more powerful state, you've now given the opposition a first to deal big damage. Flip that situation around so that you're the one getting powerful shots on them.
I don't know how applicable it is in this mode, but if you can air dribble the ball to victory, do it.
Lastly, if you see the opportunity to slam the ball down on a floor tile that's 1 hit away from breaking, you can find a means to secure the goal by contacting the ball from above to knock it against the floor, and then dodge into it right after so that it gets pushed through the floor immediately after. It is the equivalent to a backboard goal: