When playing the Arena Challenge, all players are eligible to receive back double the diamonds spent on continues when they complete the challenge for the first time.
The claim process happens automatically. The first time you complete all of your Arena Challenge rounds, you'll get all the diamonds you've spent for that challenge back in double together with the final challenge prize.
Important
1) Your account is only eligible for double diamonds back when you complete the Arena Challenge for the first time.
2) Even if you complete your first challenge without spending any diamonds on continues, you will still not be eligible to receive double diamonds back in future completions.