After just three attempts this evening (dying at about 350 and 650m on the first two attempts), I completed 1000m mode, and therefore, the game! I lost my first life at around 400m, and the second at 600m. When I got to 900m I made a dash for it, picking up just two easy-to-grab air tanks along the way, and making it with just 20% air left.
I then watched the credits, which made no sense whatsoever, and checked to see if any other modes had been unlocked. They hadn’t. So, The End!