Yes you can!

Make sure that your devices are logged in using the same Game Center ID, as it automatically saves in-game progress, also on multiple devices.

Important: You can only connect one game account per Game Center. Should you try to save multiple user accounts on the same Game Center, this might result in lost progress!

To connect to Game Center:
  1. Enter your Device Settings and select Game Center
  2. Tap on your Apple ID
  3. If you already have an account, you can log in right away. If you don't, you will need to create an Apple ID
  4. Launch Badland Brawl

After loading, a message will pop up reading “Welcome back _______” with your name filling in the blank.

From now on, your progress will be saved across device!