First things first, prepare yourself mentally. Completing the entire Dance Battle requires 5 minutes of concentration, and a single mistake results in starting all over again. There are gonna be a lot of mess-ups, and It's gonna take a lot of practice. While the goal is to do things perfectly try and just have fun, and appreciate how hilarious the entire thing is, I can't help but laugh at the way the chief dances right at the start, and that helps keeping things from becoming frustrating.

Now on to the actual Dance Battle. It's not complicated, but knowing how things work will help allot.

Rounds 1, 2, and 3 are pretty straight forward. 4 beats, with the timing getting faster on the 3rd round.
Round 4 is when things get trickier. There are 5 beats, with the 3rd and 4th being a double beat of the same color. Pay attention to the beats of the music during this round, da,da,DaDa,da That's what you want to go along with.
Now The Bonus round, seeing this for the first time made me nervous, it looks like too much to handle, but it's actually deceptive, it's more simple than it looks. There are 8 beats, but really it's 4 beats, then those same 4 beats repeated again. You don't need to worry about learning 8, since it's actually just 4 x2.

The rest from here is practice and persistence, this took me about 3 hours counting some breaks now and then, so good luck.