For this achievement it's easiest to intentionally fail a song together with your co-op partner. Pick a song you're both familiar with and play it on whichever difficulty you prefer. Easy or Medium would probably be best so it's not that hard to get past 95% of the song.
If you're familiar with the song, towards the very end both of you need to strum as fast as you can without hitting any of the colored buttons to "miss" and cause your multiplier and score to drop rapidly. Keep doing this until you fail the song and the achievement will pop.
Bright Light Fright by Aerosmith is the shortest song in the game lasting 2 minutes and 19 seconds.