SEGA Superstars Tennis

There is only one challenge in the Alex Kidd court in Superstar mode, and after winning that singles tournament you will unlock this Achievement, and the secret character Alex Kidd.

When you face off against Alex in the finals, try these strategies:

When serving, give him a couple seconds to move into place before you start your serve. He has a tendency to position himself near the outside edge of the court. Aim your serve to the near outside of the court to draw him further away from your side. Then aim your next return volley to the far opposite court.

When Alex is serving, aim your return volley to the near outside court away from the side he serves from. That will again draw him close to the net and to the far side of the court where he will be out of position for another return volley to the far opposite court.

It doesn't work all the time, but it gives you a good fighting chance if you're using a balanced or control character.

One additional thing that could be added to Vermin360's Guide:

To Unlock the Alex Kidd Stage, you must:
Complete "Survive to Score" in the Space Harrier Stage (Survive to Score is the tenth mission in the Space Harrier Stage)

To Unlock the Space Harrier Stage, you must:
Complete Doubles Match in the 'Space Channel 5' stage (Doubles match is the second mission in Space Channel 5)

Space Channel 5 Stage is available from the start of Superstar Mode, so if this is one of your last characters to unlock and you don't wish to win every challenge quite yet, follow these steps.
Play the Space Channel 5 Stage to the Doubles Match, then Space Harrier Stage to "Survive to Score", then Play the Alex Kidd Stage and You'll Unlock the Character.

Credit to Drabik for pointing out another possibility:

It could be possible that the stages unlocked are not mission specific, but rather unlocked by completing challenges with at least an "A" rating in multiples of ten. For example of this theory, Alex Kidd would be the seventh stage to unlock, meaning it would take 70 challenges with a rank of "A" or higher to unlock. I will be testing this further and update accordingly. I recommend that if you are seeking this achievement and the first method does not work, try completing 70 challenges. If anyone else confirms this either way, please message or post a comment.

I was having trouble doing this with Sonic, Ulala, Aiai, and etc. Then I tried with Dr. Eggman, and got AA on Alex Kidd's match on my first try.

Just do the same strategy you've probably been doing (hit to one side, he hits back, hit to opposite side) and you should ace this no problem.

If it's still hard, try changing the difficulty to easy in the options. And also, make sure to keep Superstar mode on. For some reason the difficulty eased up a lot when I turned Superstar mode on Full.

Good luck. :3

I must have lost to him around 20 times due to him hitting the ball above my head when I was close to the net. Finally I decided I would just hold backwards as if I was running to the back of the court and then I beat him in one try. I know it doesn't make sense but everytime you hit hold backward towards the end of the court.