Jerry is persistent, and this quality certainly helps him to achieve his goal of swimming, like the older boys did, through the tunnel in the rock.
He is persistent when he approaches his mother for goggles. "He must have them this minute, and no other time. He nagged and pestered until she went with him to a shop." Jerry feels that he cannot lose any time in working to reach his goal, and so he hounds his mother until she acquiesces to his "need" for goggles.
Jerry further displays his persistence as he commits to practicing holding his breath and doesn't rush his progress. He thought that he might be able to make it through the tunnel after a few days of practice, but "A curious, most unchildlike persistence, a controlled impatience made him wait." He determines to keep practicing and getting better so that he can be assured of success.
Finally, it is probably partly Jerry's persistence that helps him to survive the ordeal in the tunnel. He doesn't give up, although many others might; he keeps fighting to make it out, even though he is losing consciousness.