Well, I couldn't beat the tutorial. It says to press space but it seems to only give you a single little boost before you just fall to the bottom. Spent about five minutes mashing and holding different buttons and combos with no change... Either I'm a complete moron or there's something wrong with the game, somehow I think the former is more likely.
First of all thank you for trying out my game. To swim up you have to push [Space] repeatedly. Basically the swim mechanic is like the fly mechanic of Flappy Bird (One single press is a little boost upwards. To really gain height you have to press kinda fast).
If you have tried this and it still isn't working please contact me again, as this is behavior that neither me nor any of the testers experienced.