Punta Cana Dolphin Encounter. Get right up close to one of the ocean’s most lovable mammals during the Punta Cana Dolphin Encounter at Dolphin Discovery. This once-in-a-lifetime experience is perfect for all ages, thanks to an underwater platform that makes standing and interacting a breeze. Get a dolphin kiss, a hug or handshake and enjoy free time to swim with them as well. This popular experience includes a 15-minute safety briefing and 40 minutes of water time. A 15-person cap ensures a personalized experience! Book with us and Save 10%! Punta Cana Dolphin Encounter.