Since no one who got this trophy decided to guide the rest of us for these cards, I'll try to make things easier for you. After finishing my 2nd speed playthrough for gwent cards I decided to make this topic, so you guys will know exactly which cards you need to look for and where. You don't need to have all duplicates. You need to have each card at least once. Cards like Ghoul which have Muster means that you need to have all 3 cards from this Ghoul 'subgroup'. I hope that makes everything clear.
You have to look for merchants and innkeepers in order to buy cards from them. Blacksmiths and armorers will never sell cards but most of them will play with you. You don't have to play with every single merchant/innkeeper/smith in order to get other random cards because this game has more NPC's who are willing to play with you rather than random cards. You will know that you got every random card when they will give you literaly nothing for winning.
A tip from dalailama1989: "...to get some of the random-won-cards a little earlier: Before you play a merchant/innkeeper you haven't beaten yet, make a manual safegame. If your reward is a duplicate card which you don't need, reload and play again."
Tip from HellbornHunter: "When you go to arinbjorn make sure to talk to the inkeeper before having a drink with jorund and starting the contract because if you don't the inkeeper might glitch and you won't be able to buy the cards he sells (thaler and some of the monsters)."
1) Buy all cards from Elsa, the first and only Innkeeper in White Orchard. (MISSABLE)
2) Win the tutorial match of Gwent.
3) Gwent: Playing Inkeepers (you will get this mission from a noticeboard or by playing with the first inkeeper from this quest)
4) Gwent: Velen Players (the starting NPC I believe is Baron in Crow's Perch)
5) Gwent: Big City Players (one of the notice boards in Novigrad)
6) Zoltan Chivay will give you a quest "A Dangerous Game". Once you get all there cards, make sure that you keep cards instead of money. (MISSABLE)
7) Gwent: Old Pals - This one is tricky. You start this mission after defeating Zoltan Chivay who is located near Rosemary and Thyme. At some point you will need to play against Lambert. In order to find Lambert you must finish a side quest "Following the Thread". After killing Ekimmara and finishing this side quest Lambert will give you a new quest. Acept and finish it. After you finish this quest talk to Lambert straight away before he goes to Kaer Morhen. If he goes there and you don't have fast travel just play the story line quickly until you get Uma. (MISSABLE)
Here is a tip from JoaoMXN: "if you don't play Gwent with Lambert before he go to Kaer Morhen (according to the game) you can still meet him at "The Nowhere Inn". He appear on the place even if the map points to Kaer Morhen." http://i.imgur.com/h50EaL4.jpg
8) Do Triss Merigold's side quest "A Matter of Life and Death". Once you reached the ball, head to the only exclamation mark on your map and play against three players in order to get their cards. (MISSABLE)
9) Gwent: Playing Thaler. In order to find Thaler, you will need to finish side story of Triss Merigold. Dijkstra will give you "A Deadly Plot" side quest. Follow this quest until you find and free Thaler. Play against him before he leaves. (MISSABLE)
10) Puttkammer and Sweers cards can be bought from Merchant in Claywich. In order for this merchant to appear you need to free him from bandits. The bandit camp is located to the East from Boatmaker's Hut (At the centre of the big island) in Velen.
11) Gwent: Skellige Style. Find a notice board and get this quest. In order to play against Gremist you need to finish "Practicum in Advanced Alchemy".
12) There is a druid-questgiver near the previous location who gives you "Shock Therapy" side quest. Finishing this quest will get you another hero card.
Hope this helps. I will add if I find that I missed something.