In order to slay the guardians, you require [King's Resting Place Raid Tickets] instead of stamina.

There are two types of raid tickets: regular and special tickets.

1) Raid Ticket
This can be obtained from the Fallen Ancient Kingdom. Each day at 16:00 PST, the number of tickets you hold is reset to zero.

2) Special Raid Ticket
This can be obtained by using the [Heart of the Sea King]. The number of special raid tickets is not reset.