This solution is specifically for people who missed the achievement on their playthrough, and want to know what the absolute minimum game is to obtain all the cards, and handle all quest interdependencies. Caveats:
1] This is not a Gwent strategy guide, just a Traveling Salesman solution to obtaining the cards. You should already know Gwent well before starting.
2] This guide doesn't itemize the cards; those lists are available in the other solutions. If you do the following quests, in the order specified, and play/buy as instructed, you will get all the needed cards. If you want to track your cards, be forwarned, that patch v1.07 changed some of the card locations around. As an example, Midcopse cards can now be bought in Lindenvale. Trying to track specific cards to specific locations is more difficult now, as they migrate around the map in your favor.
3] Play on easy. We're only doing required quests, so you'll be running numerous levels below the suggested ones. Put your acquired abilities on Fast Attack, Strong Attack, Igni, Quen, and one on Axii and Vitality. Don't worry about side quests to level-up, you'll be fine (at least until the end).
4] Money will be tighter than usual in the beginning. Conserve it for buying cards. Don't buy any swords, armor, or potions and you'll be fine.
5] Save before and after every match. I had to play the nobleman 6 times instead of once for failing to follow this simple rule. (Game crashed during fast travel)
6] Numbers in square brackets below refer to map locations as described at: http://www.gosunoob.com/witcher-3/gwent-players-merchants/
7] Refer to http://witch3map.com
for more detailed locations of players/sellers within a town if you get lost.Kaer Morhen
- Play through the Prologue.White OrchardLilac and Gooseberries
- Beat the Scholar at Gwent
- Buy 5 cards from the Innkeeper. With the v1.07 patch, you can keep coming back to the inkeeper, and she will have another Decoy card to sell, until you get all 3 of them (for a total of 7 cards). Number of cards available at other Decoy sellers will vary, based on the number of Decoys you obtain here (the game will not exceed 3 Decoys)
- [Level 3] The Beast of White Orchard
- [Level 2] The Incident in White OrchardPalace of Vizima[Level 2] Imperial Audience
- Play the nobleman. He can be beaten with your weak deck, I did it on the first try. And again on the sixth attempt (see Rule #5).Velen[Level 5] The Nilfgaardian Connection
- Go to the Inn at the Crossroads. Buy 5 cards from the Innkeeper. Don't play the innkeeper yet; your deck isn't good enough.[Level 6] The Bloody Baron
- Buy from the Trader, Crow's Perch. Total number of cards depends on how many you bought in White Orchard; I was able to buy 4. 
- Play the Trader, Crow's Perch 
- Play Fergus the Blacksmith, Crow's Perch 
- Play the Quartermaster, Crow's Perch 
- Buy from the Quartermaster, Crow's Perch [Level 6] Family Matters
- Play merchant in Blackbough 
- Play blacksmith in Blackbough [Level 5] A Princess in Distress
- Play the Bloody Baron, Crow's Perch. You should take the Lubberkin choice, then go inside and play the Baron while the Lubberkin bakes. 
- Play the merchant in North Oxenfurt. Swim across the river on the northwest side of Oxenfurt to avoid bridge restrictions. 
- Play the armorer in North Oxenfurt 
- Play Stjepan, innkeeper at the Alchemy Inn, Oxenfurt . Play first, buy later.
- Buy 3 cards from Stjepan
- Play the blacksmith in south-east Oxenfurt 
- Play herbalist NorthEast of Oxenfurt 
- Play blacksmith in Lindenvale 
- Buy from merchant in Lindenvale 
- Play merchant in Lindenvale [Level 5] Hunting a Witch
- Buy cards from the merchant at Midcopse 
- Play the merchant in Midcopse 
- Play the armorer in Midcopse [Level 6] Wandering in the Dark
- Play the merchant in Oreton [Level 6] Ladies of the Wood
[Level 5] The Whispering Hillock
- That leaves three Players/Sellers to come back to later in Velen (Either your deck is not good enough, or your level isn't high enough)Novigrad
You need to play these Novigrad quests for 3 reasons:
1] You need to do Get Junior
to finish Big City Players
2] You need to do A Poet Under Pressure
to play at Vegelbud,
3] You need to level up to survive the first mission to Skellige.
To avoid drama at the bridges, just fast travel to the herbalist north-east of Oxenfurt, then ride up the east bank of the river to Novigrad, until you arrive at the Seven Cats Inn. Then start a massive Gwent-playing campaign:
- Buy cards from innkeeper at Seven Cats Inn 
- Play innkeeper at Seven Cats Inn 
- Buy cards from innkeeper at Cunny of the Goose 
- Play innkeeper at Cunny of the Goose 
- Play Elihal the Tailor 
- Play merchant in the market by Tretogor gate [not marked]
- Play dwarven herbalist south of Hierarch Square, across the canal 
- Play the madam at Crippled Kate 
- Buy cards at the Golden Sturgeon 
- Play the innkeeper at the Golden Sturgen 
- Play fish seller west of Hierarch Square 
- Play the merchant across from the blacksmith 
- Play blacksmith north west of Hierarch square 
- Play the bookseller in north Hierarch square 
- Buy from Olivier at the Kingfisher 
- Play Olivier at the Kingfisher 
- Play merchant near north notice board near Passifiora 
- Buy 4 cards in the Passifiora 
- Play innkeeper at The Nowhere Inn 
- Play the merchant across from the loan shark 
- Play the loan shark south west of Oxenfurt Gate 
- Play the alchemist north of Oxenfurt Gate 
- Play the priest near Elector's Square 
That's about as good as your deck will get without doing some quests. So first finish Gwent: Velen Players
- Play the Old Sage in Benek
- Play the Boatbuilder in Oreton
- Play Hadko the Card Prodigy in Midcopse
- Receive the reward card
Now finish Gwent: Playing Innkeepers
- Play Innkeeper at the Inn at the Crossroads[Level 10] Pyres of Novigrad
- Play the merchant inside the Putrid Grove area. He is unreachable until you start this quest.
- Play the blacksmith south of Hierarch Square . He has a surprisingly good Monster deck.
- Play merchant just west of the above blacksmith
Start Gwent: Big City Players
- Play Vimme Vivaldi  to start the quest
- Play the Marquise Serenity at the Passiflora [Level 7] Novigrad Dreaming[Level 11] Broken Flowers
- Play Zoltan once you chase all the leads, starting Gwent: Old Friends
- Play Vernon Roche[Level 12] Get Junior
- Play Sigimund Dijsktra
- Play Scoia'Tael Trader
- Receive card as reward for finishing Gwent: Big City Players[Level 12] Count Reuven's Treasure[Level 11] The Play's The Thing[Level 13] A Poet Under Pressure
- Subquest: [Level 12] A Matter of Life and Death
- Play for Milva at Vegelbuds
- Play for Vampire: Bruxa
- Play for Dandelion
- Subquest: [Level 12] A Dangerous Game
- Zed - obtain Isengrim
- Ravik - obtain John Natalis
- Caeser - obtain Fringilla
- It should go without saying, but when given the option of keeping the cards, or taking money, you take the cards
- Turn on the [Level 14] Now or Never Quest
. This will show you Triss's location. Suggest the sewer option to her quest. At the end:
- Accept [Level 14] A Deadly Plot
, and release Thaler. You have to play Lambert before Thaler, so you can't play Thaler yet.Velen Cleanup - Including the Claywich Merchant Solution
There are 2 hostage rescues you shouldn't attempt until you level up, and one player whose deck is too good to play until this point.
The v1.07 patch fixed the Claywich merchant bandit key drop issue (in fact, the bandit leader now has 2 keys). However, either the Merchant often doesn't survive the walk back to Claywich, or if you follow him, he simply stops walking when he perceives potential danger (he also takes a very long indirect path nearly to Crow's Perch, and then turns down toward Claywich), and completely disappears if you meditate. Here's the solution: before doing anything, fast travel to Crow's Perch. Ride down to Claywich to locate the fast travel point. Ride back up towards Crow's Perch, and then take the NorthEast fork. Take out the cowardly knight at the cluster of 3 houses (just SouthEast of the Crow's Perch waypoint). Take the South path at the next fork (go around the house), and kill the 4 bandits on the road NorthWest of Boatmaker's Hut. Take out the Monster's Nest on the West edge of Boatmaker's Hut. Head East out of town and when crossing the bridge, take the violent path in the discussion with the toll-taking bandits, and kill them all (there is a non-violent alternative, but it will mess up the merchant). Finally go to the bandit camp, which is a circular fort of sharpened logs, and Save before you get close enough to alert the bandits. Then kill all the bandits, and take the key. Save. This is the most important Save of the game
. Save. Release the merchant. Go to the fast travel pole and meditate for 23 hours, then fast travel to Claywich. I found him there in the NorthWest-most house. If you don't find him, reload your save, release the merchant again, then follow him back to Claywich. I've drawn the merchant's path here:
- Buy cards from the merchant in Claywich. 
- Play the merchant in Claywich 
- Go southwest of Mulbrydale, rescue the armorer. Then play in Mulbrydale . It should be noted that the armorer made it to Mulbrydale, and would play Gwent, but gave no card upon losing. Your mileage may differ.
- Play Yoanna the Blacksmith's apprentice, Crow's Perch . She has one of best Monster decks in the game, and is very difficult to beat until you flush out your deck.
- That completes everything in Velen. Go to Novigrad and hire a boat to Skellige.Skellige
- Turn on Following the Thread
, kill about 50 people, find Hammond, then return to the Nowhere Inn and play Lambert (back in Novigrad). This is a tad tricky. Before going into the Nowhere Inn, save. During the discussion with Lambert, say you will meet him at the next destination, and as he stands up, quickly talk to him again before he leaves in order to start the Gwent game. You need to play him here; if you miss him, you will not get another chance until near the end of the game back in Kaer Morhen.
- Play Thaler at the Seven Cats Inn (back in Novigrad). That completes everything in Novigrad except the final tournament.
- Fast travel back to Skellige, and start island hopping. You may have to take a boat to some of these locations, depending on which maps you've picked up.An Skellig (North East island)
- Play blacksmith in Urialla Harbor 
- Buy cards from innkeeper at Urialla Harbor 
- Play innkeeper in Urialla Harbor 
- Play the armorer in Urialla Harbor Hidjarsfall (East Island)
- Play the armorer in Larvik 
- Play the merchant near the inn in Larvik 
- Play the innkeeper at the House of Warriors inn 
- Play the blacksmith in Larvik Faroe (South East Island)
- Buy 4 cards from innkeeper in Harviken 
- Play the innkeeper at the Inn in Harviken 
- Play the blacksmith in Harviken Spikeroog (North West Island)
- Buy cards from innkeeper in Svorlag 
- Play innkeeper in Svorlag 
- Play merchant in Svorlag 
- Play blacksmith in Svorlag Ard Skellig (Large, central island)
- Buy from Jonas the innkeeper at the New Port Inn 
- Play Jonas 
- Play the blacksmith at Kaer Trolde 
- Play the armorer at Kaer Trolde Fayrlund
- Play the blacksmith 
- Play the merchant Arinbjorn
- Buy 4 cards from innkeeper 
- Play the innkeeper 
- Play the blacksmith  (didn't get a card from him). In fact, you should now be out of random cards, and get no additional cards from playing random players any longer. If you picked up a card here, you've missed something. In that case, continue down the west coast to Holmstein's Port and nearby Kaer Muire, where you can find 3 more players. All remaining cards will come from quests.
Go back to Kaer Trolde, and pick up the contracts on the Kaer Trolde Notice Board to start Gwent: Skellige Style
. You'll have to play through the first 2 Skellige quests to get access to Ermion:[Level 16] Destination: Skellige[Level 16] The King is Dead[Level 13] Echoes of the Past
. Technically, this is not needed to get to Ermion, but it will automatically start when you approach him. It's unavoidable, even if you turn on the Gwent quest. After this quest completes, turn on Gwent: Skellige Style
- Play Ermion
- Play Crac an Craite
- Play Sjustra the Tailor
- Approach Gremist to play, but he will give you the quest:[Level 24] Practicum in Advanced Alchemy
. This is a bugger, as I was level 16, and this is a level 24 quest. So some advice:
- For the pimpernel part, side with the Sucubus, and she'll let you pick a pimpernel without a fight.
- The distillery: ride your horse up the mountain, and move rapidly past the 3 alghouls (a level 16 witcher cannot kill level 24 alghouls - at least I couldn't). The horse will not fall off the mountain, so you can easily take a hard right when the trail ends. Quickly move into the cave with the cyclops. The horse won't go any further than the cave ramp, so get off, turn hard left, and hide under the ramp until the alghouls leave. Take out the cyclops, going back under the ramp whenever health is too low. When finished distilling come out of the cave and use the fast travel pole to bypass the alghouls.
- Foglets: these are actually killable, even though they have red skulls over them.
- Finally, play Gremist
- Play Madman Lugos
- Then receive a reward card for completing Gwent: Skellige Style
.[Level 24] Shock Therapy
. You can do this after playing Gremist, since he's just a couple of trees away, but no harm in doing it after wrapping up the madman. Don't forget to close the quest and pick up your reward card. That completes everything in Skellige, so back to Novigrad for the finale:[Level 26] High Stakes
. The only tricky part with this (other than actually winning the games) is the fist fight you need to win against a level 26 NPC. This was pretty easy by: waiting for him to swing, counter, strong attack, fast attack, roll away. Repeat. Took 3 cycles of those moves to take him down. During the tournament save anytime you have an opportunity. If you lose the fist fight, you will die, but the game will reload with an auto checkpoint made after the last gwent game, so you won't have to replay that one.
Achievement did not pop with v1.07 patch, but did pop with v1.08 patch after starting a random gwent game. I was level 18 when the achievement popped.