Hi - I recently used the following headline in a document:

Better Managing Your Health Means Better Managing Your Life

My boss wrote back that "better managing" is not grammatically correct. She's wrong, isn't she?

Better = adverb, Managing = gerund (gerunds can be modified by adverbs since they have verb-like properties, right?).

Note: in this sentence, the gerund 'managing' is the subject in the first part and the object when used the second time.

To me it's an awkward headline, regardless of grammatical rules, and regardless of who is more correct, you or your boss.

I'd use:
Better Health Management Means Better Life Management