Far in the future (1999!) humanity (i.e., Western non-Communist nations) has colonized the Moon on Moonbase Alpha, using the far side of it as a dumping ground for nuclear waste. Then calamity strikes! The nuclear waste on the far side spontaneously explodes (don't you hate it when that happens!) and the Moon is sent hurtling (intact) out of Earth's orbit at millions of miles an hour! If you can believe that, then you might find a modicum of enjoyment from this "movie".
"Cosmic Princess" is basically two non-sequential episodes of "Space 1999" spliced together, which explains the lack of continuity in the middle of the film. The first part involves our heroes being held hostage by an Orson Wells impersonator with dyed hair who controls the whole of the planet through a computer made out of bubbling beaker fluids. The crew of Moonbase Alpha (I can't remember any of their names) eventually escape with the mad scientists's shape shifting daughter, Maya, the so-called Cosmic Princess. Maya is able to take on such princessly forms as: a lion, a dove, man in a gorilla suit, man in an anthropomorphic insect suit, and her father (hair, clothes and all).
In the second half, two crew members are stranded in space and struggle to catch up to the Moon (it fell into a time warp) as Maya loses control of her shape shifting abilities and runs amok on Moonbase Alpha. Checking around on the internet, the two episodes spliced together (The Metamorph and Space Warp) are actually the 1st and 14th episodes of the 2nd season of Space 1999. I bring this up because in the 2nd half of the movie it is difficult to understand why Maya isn't just blasted away after she kills some people and starts wrecking the base.
As a MST3K episode, the riffing is OK; much better in the 2nd half, especially during the intense 5mph moon buggy chase scene near the end. It originally aired during the Super Bowl in 1989 so there are a lot of football references in the breaks during the movie.