Meepit vs Feepit avatar is pretty simple to get. All you need is just to know the right moves. Getting this avatar will take about 20 minutes or so to get.
The best way to earn points is by using the combo moves.

Combo moves:

XZXZ or
ZXZX

Since the combo moves always give you more points than the basic ones I suggest that every move you throw at your opponent is a combo.
Also doing a combo move in the air gets you more points.

When you have defeated the first meepit two times in the next round hurt him a lot until he is close to dying, then let him win. Doing this will let you have more rounds to score a lot of points on. Once both you and your opponent have two wins each beat him.

Do this for every meepit you battle and by the time the game ends you will have more than three thousand points under your belt.