The price to enter the Challenges resets after a few days, so you don't have to spend extra diamonds to participate.
The following is how long it takes until the fee resets for each Challenge:
Tier 2 - resets after 5 days
Tier 3 - resets after 8 days
Tier 4 - resets after 11 days
Tier 5 - resets after 14 days
Tier 6 - resets after 28 days
Tier 7 - resets after 42 days
Tier 8 - resets after 42 days
Tier 9 - resets after 42 days
Tier 10 - resets after 42 days
Tier 11 - resets after 42 days
Tier 12 - resets after 42 days