Provided you pay attention to what you are doing, this should not be difficult.
The way the game works is that you have a multiplier starting from x1 on each track, as you play through a track correctly hitting notes the multiplier for that track will increase. You can see when your next multiplier for each track ahead of you also.
At each checkpoint the multplier level increases based on the multiplers for the rest of the tracks. If you leave even one track at the lowest multiplier by the time you reach a checkpoint the multiplier wont increase AT ALL.
Watch the multiplers on the left. The guitar and bass tracks are at the highest levels, the drum track is one level below and the vocal track is two levels below.
So to get this achievement you MUST increase each track to the highest possible multipler between each checkpoint! If at any checkpoint the level cap does not increase by 3, you will not get this achievement.Addendum
: It may just seem that you just have to get all the instruments at the highest level by the time you reach the finish. In which case the checkpoints within the song wont matter much. If this is the case then it's vital that you pick a song that all the instruments end pretty much together. Someone will need to confirm this though.
Also if a track does not have any notes at all between checkpoints, then it will increase to the maximum at the next checkpoint. You don't have to worry about that for and its icon should appear greyed-out on the multpliers.
You get the achievement when you reach the finish.
If you are struggling with this, play an easier song with as little instruments as possible. If you only have to handle Bass, Guitar and Drums, this will be vastly easier.