La followed by agua is a glottal stop which some languages try to avoid in speech. That is why we say in English "an orange" rather than "a orange". It is also why in Spanish "a el" is contracted to "al", and in French it is avoided sometimes e.g. "l'eau" instead of "la eau". There are lots of other glottal stops with vowels following each other and most Romance languages have come up with similar workarounds to make them a bit easier to say.
Agua is feminine, however, because of this pronunciation issue with the two vowels side-by-side, it's actually 'el agua'. Since it is truly feminine, the phrase 'el agua pura' is correct. Pura needs to be in the feminine form because agua is feminine, but you'll use to masculine article el to break the double vowels.