Sea turtles can hold their breath for several hours, depending on their level of activity.
If they are sleeping, they can remain underwater for several hours. In cold water during winter, when they are effectively hibernating, they can hold their breath for up to 7 hours. This involves very little movement.
Although turtles can hold their breath for 45 minutes to one hour during routine activity, they normally dive for 4-5 minutes and surfaces to breathe for a few seconds in between dives.
However, a stressed turtle, entangled in a ghost net for instance, quickly uses up oxygen stored within its body and may drown within minutes if it cannot reach the surface.
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References:
Hays GC, Akesson S, Broderick AC, Glen F, Godley BJ, Luschi P, Martin C, Metcalfe JD & Papi F 2001. The diving behaviour of green turtles undertaking oceanic migration to and from Ascension Island: dive durations, dive profiles and depth distribution. Journal of Experimental Biology 204: 4093-4098. Hays GC, Hochscheid S, Broderick AC, Godley BJ & Metcalfe JD 2000. Diving behaviour of green turtles: dive depth, dive duration and activity levels. Marine Ecology Progress Series 208: 297-298. Hochscheid S, Bentivegna F & Hays GC 2005. First records of dive durations for a hibernating sea turtle. Biology Letters 1: 82-86. Lutz PL and Musik JA (eds.) 1996. The Biology of Sea Turtles Volume I. CRC Press.