In this sentence, can I say "day-to-day" without "basis"?
Unfortunately no, not in this sentence. "Basis" is needed in this sentence because he is discussing the routine of daily water intake. If you wanted to remove the word "basis" you would have to change the sentence. It could be "Day-to-day, maintaining a normal..." If you wanted to remove "day-to-day" you could say "daily" instead. Here are some examples of "daily," "day-to-day," and "day-to-day basis" being used in different sentences. Ex: I drink water daily. Ex: It's hard to maintain a healthy diet on a day-to-day basis. Ex: Day-to-day, I try to practice mindfulness.