Pressing up should make you go up. Pressing space can also make you go up, but up definitely should.
At first I thought hitting enter was supposed to be a timing thing, but apparently you can just hold it. Having it this way, it doesn't really add to the skill. It just makes controls more awkward. If it's not supposed to be part of the skill, I recommend getting rid of the control entirely and if you push against a wall and you're not moving up, it automatically hooks. And I'd make pressing the opposite direction automatically jump. Down could be fall, or just slide down.
I was expecting that after you get the hook sword, you'd get sent back again and have more stuff you can do. Maybe add that if you want to add more to the game with other monsters to help.