By the year 2085, World War III has left both the East and West crippled and destroyed. The major cities have been reduced to rubble, and a mechanical army known as the MME - soldiers originally created by both sides to fight in the war - has decimated the population; extinction is eminent. Though hostilities prevent the two groups from cohesively joining together to combat their now common enemy, a daring plan has been hatched that may save some of the world's population from destruction: they will be sent to the Mars Base in an evacuation. Sandy Neuman, along with other remaining military forces, must now fight the machines with all they've got so that others may escape safely to the stars...
Witness the true beginning of the Matrix: how men created the machines and how those machines stood up against their masters, and the effects of the great war that waged between them, which in the end led to the fall of mankind. Watch the ship Osiris and its efforts to warn the remaining humans of the imminent attack; follow a champion who happens to break free from the Matrix; explore the exploitation of a glitch in the overall system; observe the story of the Kid and how he was found by Neo; travel with an investigator who tracks the well-known hacker Trinity; and learn the secrets of the Matrix in other wondrous ways.
As a caveat, Animatrix is better than Rhea Gall Force in almost every way - animation, story, and overall enjoyment. Regardless, this is a decent rec based upon plot alone. Both deal with a future where machines are winning the war against humanity, and that alone makes an acceptable recommendation.
The year is 2179: humans and robots have colonized Mars. A newer Third-Type robot has been designed to interact undetected in human society. That is, until a man named D'anclaude discovers their secret and starts a movement to wipe them out. Armitage is a Third-Type that works for the police with her partner Ross, and now these two must rid the planet of D'anclaude and his evil plans.
This might be a bit more of a stretch recommendation, but if you enjoyed the generic sci fi action of Rhea Gall Force, check out the far superior Armitage III. Totally different premise, but would surely appeal to the same audience.