The Moon Zone is the extra stage in Sonic Advance. It is accessed by obtaining all seven Chaos Emeralds from the Special Stages scattered throughout the game, completing the game as all 4 characters, and then clearing the X-Zone while playing as Sonic. It consists of Super Sonic racing along the surface of the Moon and attacking Dr. Eggman, who is in a giant mech known as the Super Egg Robot (スーパーエッグロボ) (or the "Super Egg Machine" in the official Prima Strategy Guide).
The player starts with 50 Rings, and loses one per second as they go. Eggman will start off guarding the head of the mech (which is the weak point) with spiked claws. The mech will then swing both arms down in an attempt to swat Super Sonic away, and then scrape them along the ground to throw out debris that will knock Super Sonic back if it hits him. While the debris flies, Eggman will fire several laser sweeps that will cause a shockwave of explosions along the ground, which will (you guessed it) also knock Super Sonic back, wasting precious time & rings. To beat him, the player needs to dodge all of this, and hit the head of the mech to damage it. Eight hits and it's done for (which is much easier than it sounds).
There are NO Rings around to pick up to replenish the player's supply, but they needn't worry. During the fight, Eggman will be constantly launching Pac-Man-esque capsules at Super Sonic in an attempt to trap him. If a capsule grabs him, it will hold him in place for a few moments before it breaks, leaving him open to attack. However, if the player manages to make Super Sonic dash into the capsule before it can trap him, it will bust open & release some Rings for the player to collect, replenishing their supply.