From Halopedia, the Halo wiki
Paper Beats Rock is an achievement for Halo: Reach multiplayer matchmaking added to the Defiant Map Pack with the release of Halo: Combat Evolved Anniversary. The achievement was unlocked by assassinating a player that had just exited Armor Lock in a matchmade game. It could only be unlocked on a Defiant map.
Following the shutdown of Xbox 360 Halo online services on January 13, 2022, this achievement is no longer attainable.[1][2]
The achievement's name is a reference to the game Rock-paper-scissors.