Woof! Woof woof 10 checkins @ dog runs woof woof woof 30 days woof woof! Woof!
Checkin 10 times to locations categorized as "Dog Run". From the message it sounds like you also have to do this within 30 days, but who doesn't walk their dog a lot more than this?
Confirmed: This does not need to be 10 different locations.
Unconfirmed: You might be able to checkin to 10 locations tagged as "dog park".