Is this the Amphibious Assault one in San Fierro? I didn't have my capacity anywhere near maxed out, only more than 5% according to the GTA wiki.
You can increase lung capacity by swimming around underwater (press

to dive under and swim around) or by finding oysters (which you have to swim underwater to get!), There's an oyster near the footing for the Golden Gate bridge, and that'll give you the 5% you need.