The theme behind the Twin Moons being only Luna=Luna could be that despite being alone planet-wise, the two moons are always together. They serve as the bottom grouping for the sixth groupings of Star Trip's Multi mode. The mission of this grouping is "Win within 1:30!," which will let the player go to the middle Meteo if the mission is completed successfully, or if the player fails the mission, the bottom Meteo.
Although it may not look the part, this is one of the hardest missions in the game - to fail. As the final gate between two Meteos', it may seem like a foregone conclusion that clearing this would have you face Meteo, which is true. However, the Meteo you face determines your ending, and therein lies the rub.
If you're going for The Great Battle, (which you probably aren't), play the stage like you usually would; since Luna=Luna has such overall bad AI, you should be able to beat it without issue. If you want the alternate ending, The Limitless Eye, you're going to need to perform a pacifist strategy - and that's assuming Luna=Luna doesn't destroy itself first. Use a pacifist strategy for this: launch as few Meteos as you can, launch only if you need to, and send all of your attacks in short bursts to avoid overwhelming your opponent. Once the 1:30 mark hits, defeat Luna=Luna as fast as you can, then proceed onwards to what is arguably the worst ending in the game.
As a side note, if you feel like your opponent is going to lose, hold the Speeder down until you lose; if you win, you will be forced to the ending The Great Battle, and will have to come all the way back to Twin Moons to try for The Limitless Eye again.
Molten Hellions | Chlorophylls
Stray Planet | Mechatropoloids | Earth Lovers
Bubblies | Dimensionals
Electric Nymphs | Hot & Chillies | Clean Air Club
Twin Moons | Illusionists | Rare Cultures
Meteo | Hevendor Realm