Loving the game so far, and it feels great to play! However, I feel the game was not designed around the achievements. I've been going for multiple runs trying to beat it without heart producing units, but I get overwhelmed at every moment. I either get a lucky draw at the start, or I'm forced to restart the run, due to not having enough crowd control.
Recently got to the third world, and in the first actual wave I lost all of my units immediately. There was nothing I could do, there's too few units and too many mechanics to actually complete this challenge reliably.
Try to first pass all stages With producing hearts and picking useful babies/items for no heart play. When you beat third boss and there starts second loop(first levels again), it's easier to play with collected items and proper babies for your strategy. Basically, you don't have to pass all 3 arcs without chads from the start, you just need to pass them, so even if no-heart after 3 or 4 loops to get all you want, it's fine.