Not too difficult of an achievement. Here is what I did. I stood at the very bottom level and waited for the enemies to come to me and I made sure I was higher than them when we hit so they would be defeated. Repeat this for the other two enemies (3 total) and the achievement will unlock as soon as the level is cleared.
I have attached a video where the user has beaten wave 1 without dying so you can watch the video if you need additional help!
Note: If you are going to vote negatively please comment or PM me first as I am willing to adjust anything that needs to be for this to be proper.