The Triple Team achievements involve beating a certain number of NPCs at Triple Triad. The final one being Triple Team III which requires beating 41 NPCs.
I'm currently waiting for my girlfriend to catch up with me on the main storyline and as yet have not completed the "Heavensward" quest, which means that at this point there are 37 NPCs available for me to play Triple Triad with.
For a while now I've been stuck on 36/41 on the progress towards unlocking Triple Triad III, so I've now gone through the 37 NPCs available to me and beat them all (again). During this process none of the 37 NPCs had the Triple Triad symbol above their head, which I believe is an indicator that I've beaten them in the past.
I don't know if this is a bug or if it's intentional, and I can't really guess which NPC it may be. For reference, these are the 37 NPCs available to me at this point (bearing in mind that I never beat Tataru Taru in 2.55 who is no longer available to play Triple Triad with - if that was the case there should be 38, not 37):
Code:
Lewena - Gold Saucer (4,6)
Noes - Old Gridania (10,5)
Yellow Moon - Ul'dah - Steps of Thal (14,13)
Wawalago - Limsa Lominsa Lower Decks (8,15)
Yayake - Ul'dah - Steps of Nald (7,12)
Triple - Triad Master Gold Saucer (4,7)
Jonas of the Three Spades - Gold Saucer (4,7)
Maisenta - New Gridania (11,11)
Roger - Central Thanalan (19,20)
Memeroon - Upper La Noscea (14,24)
Guhtwint of the Thee Diamonds - Gold Saucer (4,6)
Mother Miounne - New Gridania (11,13)
F'hobhas - Central Thanalan (23,13)
Wymond - Ul'dah - Steps of Nald (9,8)
Momodi - Ul'dah - Steps of Nald (11,9)
Trachtoum - Lower La Noscea (35,15)
Helmhart - Eastern Thanalan (20,21)
Mimidoa - Lower La Noscea (25,34)
Joellaut - Coerthas Central Highlands (13,15)
Fufulupa - Western Thanalan (22,17)
Baderon - Limsa Lominsa Upper Decks (11,11)
Aurifort of the Three Clubs - Gold Saucer (4,7)
Piralnaut - East Shroud (17,26)
Sezul Totoloc - North Shroud (24,23)
Landenel - South Shroud (16,28)
Ruhtwyda of the Three Hearts - Gold Saucer (3,7)
Buscarron - South Shroud (19,19)
Ourdilic - Coerthas Central Highlands (6,22)
Marcette - Central Shroud (16,18)
Hab - Southern Thanalan (24,40)
Vorsaile Heuloix - New Gridania (9,11)
Swift - Ul'dah - Steps of Nald (8,8)
R'ashaht Rhiki - Limsa Lominsa Upper Decks (13,12)
Gegeruju - Eastern La Noscea (33,30)
King Elmer III - Gold Saucer (3,7)
Rowena - Mor Dhona (21,5)
Indolent Imperial - Mor Dhona (11,17)