Adult leatherback turtles are large animals that have few natural predators. The most vulnerable stages in a leatherback's life are their early life stages at which point they are most vulnerable to predation of all kinds. Birds, small mammals and other opportunists are known to dig up nests and consume eggs. New hatchlings are also vulnerable on their journey from nest to sea. Shorebirds and crustaceans are known to prey on the turtles scrambling for the sea. Once they enter the water they become prey to a whole new host of predators such as predatory fishes and cephalopods. Very few survive to adulthood.
I believe tiger sharks eat adult leatherbacks.