Yeah there's no way to climb up the wall to escape the underground tunnels, you have to go through the flooded tunnels.
Some tips:
- Slugcat once underwater drifts upwards as to find air as quickly as possible, so you'll have to go down to keep your momentum;
- It takes 7 seconds for slugcat to drown, slugcat becoming visibly shakier as you reach the end of the 7 seconds;
- The first air pocket is the hardest to reach and the hardest part of the underground tunnels by far (after that, air pockets become more plentiful and closer to each other);
- To deal with leeches, you can stun them by throwing one of those snail-turtles (they stun you as well if you're too close), you can wait outside the water for them to dry off and to detach