There are 88 total screens; the Crash Site screen does not seem to count. To visit all of them, besides from visiting the usual screen, jump around and visit a few screens that do not have names. Note: Do not skip the Treemen's Domain.
The three heart containers are found at the indicated locations: (Screenshot 2) (Screenshot 3)
You must find a certain number of different screens. Pass through all the cores, artifacts and secret locations. Make sure to telejump out of screens when possible. Jump as far as possible to reach the furthest position of every screen to check for hidden locations.
Do not any checkpoints after dropping down to the Alien Outpost. Hit the checkpoint located here , collect the Gauss Gun, then intentionally die. Go up and reach the top right part of the secret cliff (Screenshot), then kill the Chomper to get the upgrade for the Gauss Gun (Screenshot).
Walk back and forth at the end of a screen to the next one repeatedly.