NieR: Automata offers optional DLC content, including the universally available 3C3C1D119440927 pack, featuring additional challenges and cosmetic rewards. After some game progress, a Mysterious Letter unlocks three colosseum locations, each with six increasingly difficult ranks.
Trial of the Sand Colosseum:
Located in the desert, access this colosseum via the Desert: Center access point. Zoom out and locate the orange diamond-shaped structure to the right of your entry point. Awaiting you inside is the Trial of the Sand Colosseum quest.
Gambler's Colosseum:
Starting from the Flooded City: Coast access point, follow the coastal path (similar to the route used to protect the resource ship). At the path's end, locate a waterfall and circle around the building to the left. A Resistance member guards the entrance; bribe them with 1,000 G to enter and begin the Gambler's Colosseum quest.
Underground Colosseum:
This colosseum is accessible only while playing as 9S. Begin at the Forest Zone: Center access point. Follow the left forest edge until you find machines training near a large waterfall. Pass through the waterfall to access the Underground Colosseum quest.