NieR: Automata's 3C3C1D119440927 DLC unlocks three challenging Colosseums. After receiving the Mysterious Letter, you'll need to locate these arenas to access unique rewards. Here's a guide to their locations:
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Trial of the Sand Colosseum Location
This coliseum is situated in the desert. From the "Desert: Center" access point, look to the right (facing the direction you entered from) for an orange diamond-shaped structure. A machine guards the entrance, but poses no significant threat. Completing this coliseum offers the Destroyer Outfit (A2) as an S-Rank reward.
Gambler's Colosseum Location
Located in the Flooded City, access this coliseum from the "Flooded City: Coast" access point. Follow the coastal path used to protect the resource ship. At the path's end, locate a waterfall. Circle around the building to the left of the waterfall; a Resistance member guards the entrance. Bribe them with 1,000G to enter. The Revealing Outfit (2B) awaits as the S-Rank reward.
Underground Colosseum Location
This coliseum is accessible only while playing as 9S. Begin at the "Forest Zone: Center" access point. Follow the left edge of the forest to a group of training machines near a large waterfall. Pass through the waterfall to gain entry. The Young Man's Outfit (9S) is the S-Rank reward.