You can get to the Legendary Gym from the Lake of Ice area, via Kulon Mine. The Legendary Gym becomes accessible once you obtain the DigiEgg of Knowledge in the Amaterasu Server, after defeating the Qing Long and Zhu Que Chiefs.
Getting to the Legendary Gym (Step-by-Step)
Start by heading over to Kulon Mine.
Step 1: From Kulon Mine’s entrance, head north and then turn east at the first intersection.
Step 2: Continue north past the intersection. Walk past the first ladder, and then climb up the second ladder, at the end of the path.
Step 3: After climbing up the ladder, turn west and walk up the wooden ramp, then turn west again at the top of the ramp.
Step 4: Having turned west at the top of the wooden ramp, continue west past the ladder. Turn north once you get to the next wooden ramp, and then continue north towards the narrow path leading to the Lake of Ice area.
Step 5: From Lake of Ice’s entrance, walk forward and then turn northeast at the intersection.
Step 6: Continue north along the narrow linear path, then turn west past the kicking trees and walk down the wooden ramp. Then, turn southwest and continue past the Guilmon.
Step 7: Head west and then north along the narrow linear path, then continue northeast to the wooden ramp.
Step 8: Walk up the two wooden ramps, then turn north and head inside the dragon-shaped building to enter the Legendary Gym area.
Step 9: Walk a short distance north from the gym area’ entrance, then turn west and jump down the ledge.
Step 10: After jumping down the ledge, keep going west until you get to the stairs at the end of the path. Then walk down the stairs and continue past the gate to access the Legendary Gym.
The Legendary Gym is the only one in the game that offers all Super Training courses without requiring a Platinum/Gold ID, making it the best option to train your Digimon in the late game.
