The Crystal Gems search for the monster on Mask Island at the beginning of "Island Adventure". Later on, the monster attacks Lars, Sadie, and Steven, causing Steven to summon his bubble to protect them. Sadie subsequently defeats the monster by stabbing her through the torso with a spear and her gemstone is bubbled by Steven.
Her gem is seen in Rose's Fountain (along with the other corrupted gems), therefore she is currently uncorrupted.
As her corrupted name suggests, Moonstone's body is invisible, except for her gemstone. Her features become visible when substances such as mud or water coat her exterior, revealing her to have a bulky body, strong build, two eyes, and a mouth. She doesn't appear to have a distinct head or neck. Located on her chest is a cone-shaped gemstone with a slightly elevated base. While the cone portion is a consistent dark blue, the base is separated by an elevation and contains differing shades of blue. Moonstone appears to prefer walking on all fours rather than upright.
Invisibility: Moonstone's primary ability is, as the corrupted name suggests, invisibility.
Stealth: With her invisibility powers, Moonstone is skillful at stealth, as the Crystal Gems thought she escaped from Mask Island.
Enhanced Strength: She is incredibly strong, with enough power to push Steven's bubble, with Steven, Lars, and Sadie inside, over a cliff. She is also able to easily pick up and knock around Sadie during their scuffle.
Moonstone is the first Gem known to have been poofed by a human. Sadie was able to poof it with only a sharpened stick. This proves that early humans could have posed some trouble for the colonizing forces from Homeworld.
Moonstone's gem is the first shown example of a gem having more surface area hidden inside the body than exposed outside. Due to the gem's rotation, it forms a spike pushing into the hard-light body.
Her name was revealed in Steven Universe: End of an Era.
The concept art of her uncorrupted form has a face similar to the masks of the fish and worms seen in "Island Adventure". This implies that these creatures are actually smaller versions of herself that she created while corrupted, similar to Nephrite, Blue Chalcedony and Bixbite.
If this is the case, then that would make her the first formerly corrupted Gem capable of creating organic copies of herself, as they did not poof after being stabbed, and later eaten, by Sadie.