To obtain this achievement, you must defeat 100 unique card duelists in a game of Tetra Master. Some NPCs can be rechallenged, and I believe this specifically refers to the Card Arena in Treno, as I lost my Madeen card and spent many matches trying to win a new one there before popping the achievement a little while later.
It is possible to gain this achievement from not playing a single game until Disc 4, although it is advised to play some in every town you come to in order to mark off a few wins, collect better cards, and overall get better at the game.
A big thanks to the author of the Google doc linked at the bottom of this post for the list below. The author admit there are some more that they were unable to find on Disc 4, but this list comprises 99 duelists, so finding one on your own isn't too bad.
Names in square brackets may not always be present, or may leave the screen. Exit and re-enter in this case.
Alexzandria - Main Street 1
1. Old woman (next to Ilia)
2. Ilia
3. Old Man (next to Ilia)
4. Immigrant from Lindblum
Main Street 2
5. Michelle
6. Nikolai
7. Ovenmeister
Square
8. Ryan (running)
9. Man (left)
10. Tour Guide
11. Shopkeeper
12. Tom’s Mother
Inn
13. Red Mage
14. Red Mage
15. Fish Man
Alley
16. [Synthesist]
17. [Ashley]
Steeple
18. Old Lady
19. Flower Girl
20. Weimar
21. Retired Boatman
22. Boatman
23. Tom
Treno – Gate
24. Thug
25. Noblewoman
26. Nobleman
Treno Slums
27. Mario
28. Natalie
29. Thug
30. Shopkeeper
31. Carpenter
Pub
32. Barkeep
33. Thug
34. Waitress
Knight’s House
35. Drunk
36. Old Man
King’s House
37. [Nobleman]
38. [Noblewoman]
Card Stadium
39. Father
Bishop’s House
40. [Adventurer]
41. [Nobleman]
42. Noblewoman
43. Young Noblewoman
Synthesist
44. Scholar
45. Shopkeeper
Queen’s house
46. Female Adventurer
47. Criminal
Queen’s house – inside
48. Queen Stella
49. Servant
Walkway
50. Girl
Tot Residence
51. Tot
Dali – Wpn. Shop
52. Part-time Worker Mary
53. Part-time Worker Jeff
Windmill 1F
54. Trude
Lindblum – Main Street
55. Young Lady
56. Craftsman
Shopping Area
57. Oliver
58. Joanna
Residence
59. Card Freak Gon
Square
60. Carpenter’s Apprentice 2
B.D. Station
61. [I.D. Engineer]
T.D. Station
62. Attendant
Station Area
63. Card Boy
64. Card Freak
Studio
65. SPA Michael
Daguerreo – Entrance
66. [Adventurer]
67. Booklover (Accessed from 2nd floor behind old man)
68. Bookworm (Other side from Booklover)
Left Hall
69. Adventurer
70. Weaponsmith
2nd Floor
71. Librarian
72. Old Man
73. Scholar
74. Engineer Zebolt
Right Hall
75. Scholar
76. Synthesis Expert
Mage Village – Entrance
77. Nameless Tailed
78. B.M. #24
Water Mill (Chocobo hatchery)
79. Nameless Tailed
80. B.M. #33
Inn
81. B.M. #234
82. B.M. #123
83. Nameless Tailed
Pond
84. B.M. #44
85. Nameless Tailed
86. B.M. #189
Synthesis
87. B.M. #192
Cemetery
88. B.M. #56
Chocobo’s Paradise
89. Gold Chocobo
90. Yellow Chocobo
C.P. (near fat chocobo)
91. Red Chocobo
92. Fat Chocobo
93. Teal Chocobo
Mdn. Sari – Kitchen
94. Lani
Memoria – Stairs of Time
95. Master Phantom
Recollection
96. Defence Phantom
Lost Memory
97. Strong Phantom
Time Warp
98. Rare Phantom
Stairs
99. Dark Phantom
(
https://docs.google.com/document/d/1bLD1m1YyEIPOBDoRLsRH3Nwz...)