Japan had their shot last weekend, North America's up. (UPDATE: Europe too, with a discount!)
Nintendo has begun emailing their newsletter mailing list in North America to send out codes for a private Zelda: Tri Force Heroes beta.
The beta times are scheduled for particular times this weekend, and the email gives one code to the recepient and two to give to friends to test the three-player game.
Like the Splatoon testfires, online sessions are scheduled for limited times: Friday and Saturday night from 5 p.m. - 10 p.m. Pacific time (8 p.m. - 1 a.m. Eastern) and Sunday from 7 a.m. to 12 p.m. Pacific (10 a.m. - 3 p.m. Eastern) with unlimited local play. Japan received the beta last weekend, and Eiji Aounuma participated in one session.
UPDATE: The beta will be in Europe as well, as codes have gone out. Participation in the beta will yield a 10% launch discount from a digital copy of the game. Online sessions will be 17 October 8 a.m. - 2 p.m. BST, 18 October 11 a.m. - 3 p.m. BST and 24 October 8 a.m. - 2 p.m. BST.