During gameplay, find a fire hydrant or toilet. Destroy it, and stand next to the flowing water coming from its remains. Press the 'B' button, and your health will slowly regenerate, and go back up.
To unlock the hidden level, Going Down, obtain all of the time machine pieces before reaching the level, The Rack. After using the cyborg alien's head to unlock the door near the end of the level, there should be a second portal that has a fully built time mahcine in it, and this room should be adjacent to the first portal room. It is possible to replay this level to unlock the hidden level if time machine pieces are missed during a first play-through of the game.
In the third level, Nuclear Winter, you can unlock the hidden level, Wetworld. At the end of the level as you are crossing the raised train tracks, to get to the signal transmtter, if you look down while moving across the tracks, you'll see a medkit on one of the roofs. Jump onto the roof, then jump into the water and swim until you come to the platform and end-level icon.