Ever play Rhythm Heaven or another rhythm game? They will help you out with finding the beat of a song a ton. Basically what you are looking for in a song, at least in Mother 3's case, are the drums, bass, and melody of a track. Usually, you will instantly know which instrument to follow, as they tend to stand out amongst the others so you can hear the beat better.

Usually (not always) beats follow a pattern of "1-2-3-4", over and over. Although in Mother 3's case, the battle music becomes much more difficult later on because it changes the time signature of songs or the tempo of a song, sometimes even multiple times during the battle music.

To give you an example of what I mean, listen to the heartbeat of "Mr. Batty Twist". This song is one of the few battle tracks that follow a "normal" pattern and sticks to it throughout the entire track.

https://www.youtube.com/watch?v=YjDI3SiLxFs

Once the heartbeat begins, count each heartbeat until you reach 4, then repeat. That's all there is to the Mr. Batty track. You would hit the combo on each heartbeat, aka each number of the "1-2-3-4" over and over to a maximum of 16 combo hits.

But it's not always this simple. Listen to the battle song "Fate". This song follows a very different structure compared to the last...

https://www.youtube.com/watch?v=LUbgYuYKfUA

In this song, the concept is the same as Mr. Batty, but it's not following a set 1-2-3-4 pattern. Instead it's pattern is more along the lines of "1-2 1-2-3 1-2-3-4 1-2"