You can easily find hidden rooms by shooting randomly at walls as you pass them. If a hidden room is present, your bullets will pass through the wall.
Plan where you engage the aliens. Most will stop and fire without pursuing you, so give yourself some room to run backwards or jump over their bullets if you can.
Upgrade to the uzi as quickly as possible. While weak, it will occasionally fire bullets downward. This allows you to sporadically hit aliens on the platforms below you.