Gears of War 4

Crafting a Legendary card is going to take some time. As of now, there are no shortcuts: every Legendary card currently in the game costs 2,400 scrap metal.
Scrap metal can be obtained by destroying cards from packs. Packs can be bought in the store using credits. Credits are rewarded after every Versus match and after every 10th Horde wave, and also for reaching certain levels.

Unfortunately, having one of the Pre-order, Beta or Season Pass characters/weapon skins that are labelled Legendary will NOT give you the achievement. You have to craft one of the other Legendary cards yourself.

Destroying cards:
You can destroy cards using the Versus, Horde or Customization menu.
-To destroy Bounties, select either Versus or Horde from the main menu and go to ‘Manage Bounties’. and are used to cycle between Versus and Horde specific bounties. Press to show your owned cards. Next, select a card that you want to get rid of and press , then confirm its destruction to obtain scrap metal.
-To destroy Horde skill cards, select Horde from the main menu and go to ‘Class skills’. Follow the same instructions as above.
-To destroy Characters, Weapon Skins, or Emblems, select Customization from the main menu. To access Emblems and characters from the Swarm faction, use and . Follow the same instructions as above.

Scrap metal: Loss / Gain
-Common cards: Create -40 / Destroy +5
-Rare cards: Create -100 / Destroy +20
-Epic cards: Create -600 / Destroy +150
-Legendary cards: Create -2400 / Destroy +600

Buying packs with credits:
To buy packs, select ‘Store’ from the main menu. There are currently 4 packs that can be bought with credits. In addition, each of these packs can also be bought using micro transactions if you’re unwilling to spend your time grinding for credits. This achievement is going to take a while either way though, so you might as well just play the game.

List of packs that can be bought with credits:
-Operations Pack (1000 800 credits)
-Horde Booster (400 credits)
-Versus Booster (400 credits)
-Elite Pack (4000 3500 2000 credits)
-Feature Pack (4400 2000 credits) Only available during special events

Equal values (4000 credits):
-10 Horde or Versus Packs: minimum 250 scrap metal (10 x 5 x 5).
-5 Operation Packs: minimum 125 scrap metal (5 x 5 x 5) --- guaranteed: 2 Customization cards (Common or better).
-2 Elite Packs: minimum 80 scrap metal (2 x (1 x 20 + 4 x 5)) --- guaranteed: 1 Rare or better, with a greater chance of a Legendary.

Each pack contains 5 cards. You’ll want to buy the cheapest packs to maximize your profits, which would be the Horde and Versus Booster packs (400 credits each). If you only care about this specific achievement, you can go ahead and destroy every single card earned from packs.
However, if you want to work on your Horde achievements at the same time, I highly suggest buying the Horde Booster pack, and destroy any earned bounties, or skill cards from classes that you’ll probably never use.
(!) Update 5 Nov 16: Horde and Versus packs now include one guaranteed customization card.
HolyHalfDead has reported that he managed to obtain 4 Legendaries and 1 Epic card from 5 different Horde packs. So if you had any doubts about buying Horde (and Versus) packs before, it's definitely the way to go!
(!) Update 10 Jan 17: Elite Packs have been reduced in cost once again and are now available for purchase for just 2000 credits instead of 3500.
The type of pack you're buying is no longer as important as it used to be, as the packs are now much more in line with each other with the current cost/payout ratio.
Even though it might be your safest bet to go for Horde and Versus Packs on paper, there's a better chance of a Legendary (and I assume therefore Epics as well) dropping from Elite Packs according to the game's description of said pack. It's also very unlikely that an Elite Pack will only drop 4 commons and 1 rare (which is the guaranteed minimum): you're definitely more likely to end up with at least a couple of more rares. Long story short:
---Safe bet: Horde and Versus packs
---Risky bet with potentially higher payout (less risk since update): Elite Packs (or even Operations Packs)

List of achievements that you might want to work towards before destroying cards:

Buying Legendary cards:
As of writing this, Legendary cards can only be found in the character selection or weapon skins selection. There are currently no Legendary bounties, Horde skills or emblems.

List of Legendary cards:

If you vote this down, please tell me why so that I can improve this guide.
Hope this helps and good luck, it’s going to be a grind!

Just one more moment: once your Legendary card is crafted for 2400, and achievement unlocked, you can then scrape it and refund some 600 back, which reduces your total loss after all.
Also the achievement stacks with this one: