The versus button not showing up for some players is currently a known issue in the game. To participate in Versus events, first try:
1. Tapping the Profile button under the level bar on the top right of your screen.
2. Then, tap the "Fight" button on the screen that pops up.
If that doesn't work, you may able to see the Verses button by visiting another area or Cove. The Versus button should then appear there and sometimes also in the Main Cove when you go back to it.