Use your speedup ability to negotiate the maze faster, but save some of your energy in case you collect a bomb. You do not have enough time to dispose of a bomb running at normal speed.
If a monster is sitting on the weapon start button, only return it to the monster pit when it is convenient to you, as the monster does no harm except drop the pieces of the weapon to the floor. Once the monster is removed the pieces are easy to replace on the blueprint.
There is never more than one piece of the blueprint in a house, so do not return if you have already collected a weapon piece. There will only be a bomb located there.
The firing pattern of the weapon is random, and only a few shots will actually reach the top of the screen. It will therefore be mainly luck when you kill the monster.