You only need 4 badges in Sinnoh to start the battle with Shaymin after you've acquired 144 tablets and have caught the 12 alphas from the pillars of light.
Shaymin will be level 70 and your pokemon will still abide by the level cap in the battle (LVL. 37 at 4 badges).
It's still doable and an easy catch with the level cap if you just bring pokemon below with focus sash:
Memento: Smeargle, Yamask, Cottonee
Endeavor: Cottonee
Thunder Wave: Electrode
Tank/Damage: Gyarados