Ok. This will come down to personal preference a bit, but I'll give some thoughts on which levels are "best" or why other levels are "bad".
Level 1
The only problem I have here is the Jellyfish boss. I thought the level itself was the most straightforward (besides some of the projectile enemies), but the boss I was a little unsure of. I think with practice this could be the easiest combination.
Level 2
This is the level I did it on. The boss can be annoying, but I found the level to be the most consistent. Just be careful on the electric enemies. I found jumping on them and then whipping was best, but it takes some practice to get the timing right.
Level 3
Easiest boss, but worst approach. The two sections that make this a bad choice are the sombrero enemies and the helicopter hat enemies. I could manage the sombrero enemies, but the helicopter jumps were inconsistent at best. If you're good at that, then go for it, but otherwise I'd skip this one.
Level 4
Not bad, but the autoscrolling train section moved too quick for me to get it consistent. What makes a lot of the levels easier is that it's at your own pace. That autoscroll removes that safety. Boss is easy though to do damageless.
Level 5
Nope. Boss is hard to do without taking a hit already and the level itself has a few bad sections with trying to avoid fireballs. Also, I found that one of the jumps I kept bonking my head on the ceiling and dying. Overall this is a terrible level to attempt. Probably the hardest for this achievement out of all of them.
Overall, either Level 1 or 2 will be your best bet. Will probably take some practice, but with a bit of time, definitely doable.