How do you beat Boom Boom in Mario Tennis Aces?

Boom Boom is not a particularly difficult opponent, compared to the others. What makes him more challenging are the Mechakoopas roaming around.

Dealing with the Mechakoopas

Don't pay too much attention to them. Mechakoopas are slow, take a long time to detonate, don't block your way, and they can be sent to the other side of the court too.

Just keep moving around the court, so they'll keep chasing you or detonate somewhere safe. Simply keep moving forward and backward, so you can remain where you expect the ball to land. Boom Boom occasionally uses Lob Shots, but rarely (if at all) Drop Shots, so moving away from the net is relatively safe.

If you know where the ball will land, and there are Mechakoopas there, try to hit the ball with the Mechakoopas right in front of you. This way you can send them to Boom Boom's side with the ball. Boom Boom never sends them back, so don't hesitate to send him Mechakoopas if you can, but don't make this your priority!

Dealing with Boom Boom

Boom Boom is not a particularly difficult opponent, but he's not so easy that you can land Service Aces, Return Aces, or Drop/Lob Shots easily. And since your side of the court is slowly getting flooded with Mechakoopas, you want to get a point off Boom Boom as quickly as possible to clear the court.

Like I said before, don't worry about the Mechakoopas too much. Relax, and try to get as many Charge Shots in as you can to fill your Charge Meter. Try not to waste your Charge Meter on Zone Shots. Instead, try to fill it to the max, so you can use your Special Shot. If Boom Boom uses his Zone/Special Shot, don't hesitate to counter with Zone Speed.

The best way to deal with Boom Boom is to bait him into using his Zone Shot (to drain his Charge Meter), and counter with a Special Shot (or Zone Speed if your Charge Meter isn't full yet). Special Shots aren't easy to block, and instantly break the opponents racket if the opponent didn't block properly. Because of that, you want to aim your Special Shot near Boom Boom to break his racket.

Try not to use your Special Shot as soon as you can. When you do, you drain your Charge Meter. In the worst case, you'll end up with not enough Charge to counter Boom Boom's Zone Shots, which will allow him to gain many points off you in quick succession. Instead, use your Special Shot specifically to counter Boom Boom's Zone Shots.

If your Charge Meter is full and Boom Boom won't use his Zone Shot, try a Lob Shot (A -> B or forward X). This will cause a Star to appear on Boom Boom's court and gives him an opportunity to use his Zone Shot.

Eventually, Boom Boom will run out of rackets and lose by KO.