I like the concept of having two players at one keyboard able to kill each other.
However, the shooting of both being completely evened out leads to both just standing there and hitting space and enter without moving.
A fix to this situation would be an energy bar which only allows 3 - 4 shots (1 energy per shot) and refills one energy per second. This would create situations where one player is out of energy and the other can jump through the enemy´s shots unharmed.
Even better would be if holding the space / enter key would draw more and more energy, making the shot stronger, and releasing it automatically once the energy is empty - similar to Samus Aran´s charge beam (in the smash brothers games series, you can find plenty examples via youtube)