Simply use a dog on a punk guitarist. The punk is the "watermelon" of this game, and will make the dog disappear.

For this, the store page made it sound like you need a single punk rocker. I thought it would be impossible

But all you will need to do is play Dog Challenge mode on each level and "win".
To "win", you must avoid the pre-placed dog(s), and reach the electrical wire to end the round.

All of these are calculated at the end of the round. If you meet the condition when it ends, you are granted the achievement.

Highest and lowest scores are probably obvious, you can get all of a set at once with a high or low enough score.

Have X number of Y musician, some are certainly easier then others. Just keep trying.

Have all 10 at once, again this must be when the round ends.

Lastly, the achievement for all other achievements will pop whenever you get the last one.