Healthily. The word is "healthily".
"Healthily" is an adverb, which modifies the verb "eating". "Healthy" is an adjective, which just leaves the reader asking "eating healthy what?".
This has been your daily grammar fact. Cheers!
Today's the day you add flat adverbs to your grammar info, and hopefully begin on the path of gaining enough knowledge about grammar makes nitpicking on the internet seem like a bad idea
https://en.wikipedia.org/wiki/Flat_adverb
I didn't know about this, so thank you! To raise more awareness I feel like we should rebrand "flat adverb" to "flatverb" or "fladverb". This would sure be an improvement over the current brand.