Queen Serenity used it to trap those from the Negaverse inside the power of the crystal, but doing so cost all her strength, resulting in her death.
When Sailor Moon transformed into Princess Serena for the first time, she used Cosmic Moon Power to blast Zoycite into a wall, defeating her. This was the last Sailor Moon ever saw of Zoycite, as Queen Beryl later killed her.
As Sailor Moon, she also used the attack to fight off Malachite, twice. The first time, Malachite's attack was stopped, and he was left with the knowledge that he had failed to defeat the Sailor Scouts and Beryl would likely punish him. The second time, Malachite appeared to be weakened from it, and threw a powerful energy blade at her, but she reflected it back at him, killing him.
The last time Cosmic Moon Power was used was when Princess Serena was fighting Queen Beryl, who at that time was merged with the Negaforce to become a giant Beryl with more power than before. The other Sailor Scouts powered her up, and she used Cosmic Moon Power to form a giant energy ball, which completely destroyed Beryl and the Negaverse itself.
Cosmic Moon Power hasn't been used since, at least by that name, though it is possible two variations of the attack were used. In Sailor Moon R Episode 41, Final Battle, Princess Serena and Princess Rini use "Moon Crystal Power", powered by the two silver crystals (one of the present and one of the future) to destroy Wiseman. In Sailor Moon S, Sailor Moon uses an attack called "Moon Cosmic Power" in an attempt to destroy Pharaoh 90 as he makes his way toward Earth, shooting an energy beam at him, but he was unaffected and countered with a giant red energy beam.