Check the Johto region restriction
Only Johto League members count toward the member threshold. Kanto members do not substitute for them. Challenges that specify Johto companions must also be completed with Johto companions.
Complete the tower battle and capture requirements
Capture means successfully catching all three beasts. Defeating them or filling their tracking gauges does not replace this requirement.
The final battle is against Ho-Oh atop the Tin Tower, on Hard and with Johto companions. Check Ho-Oh’s own challenge for the required location and difficulty.