Question: how to beat the elite four with one pokemon project pokemon?
Answer: Use 2 Calm Minds then use Aura Sphere on her Pokemon (If her Dewgong uses Toxic, wait until her Mamoswine to use a Full Restore, as the Dewgong and Walrein will most likely use more Toxic on you). ... 
Use 3 Calm Minds then use Psystrike on his Pokemon EXCEPT for his Gallade, for that use Shadow Ball (If his.