This one shouldn’t be too much of a challenge: five IPA beers of any of the various styles. The badge goes up to level 100, that’s 500 IPAs so get going.

There are 26 styles of IPA that currently recognised by untappd: American, Belgian, Black/Cascadian Dark Ale, Brett, Brown, Brut, Cold, English, Farmhouse, Fruited, Imperial/Double, Imperial/Double Black, Imperial/Double Milkshake, Imperial/Double New England, Other, Milkshake, New England, Non-Alcoholic, Quadruple, Red, Rye, Session/India Session Ale, Sour, Triple, Triple New England and White / Wheat. Note APAs don’t count as they are classed as Pale Ales.
There are also separate badges for Black, Hazy, Milkshake, Session and Triple IPAs.
Originally the badge was introduced in 2011 as a collaboration with another website and was limited to only five specific IPAs: Dogfish Head’s 60 Minute IPA, Bell’s Two Hearted IPA, the New Belgium Ranger IPA, Sierra Nevada’s Torpedo Extra IPA and the Bear Republic Racer 5 IPA. A pretty good starting point if you ask me!