Turtles, like all reptiles, have LUNGS! They have to breathe air. They must come to the surface to breathe. They can go anything from a few seconds to several hours (when they sleep) to several weeks (when they hibernate in winter) without extra air. They also store air in their cloaca. They particularly draw on this air during hibernation. So, how does this work? All tissues are more or less permeable to various molecules. In the lungs, capillaries are as close to the surface of the body as possible, they practically "touch" the air. Exchange of O2 and CO2 easily takes place through the skin. Gills work in the same way, just in water. Intestinal tissue also has a lot of capillaries close to the surface for the purpose of absorbing nutrients. However, since the gas exchange is simple osmosis, nothing prevents this (or any other tissue high in capillaries) from also taking on O2. For example, we all breathe through the skin, even in water! If a human's skin was completely covered to make it air-tight, the human would suffocate. If your turtle does not have access to air, he will drown.