Neoverse

TL;DR
Buy cards out the store unless they're more than 200 gold and always take the missions that reward cards unless there is one for gold (or maybe something like extra Mana). Always try and kill your enemies to exactly 0HP, for the 50 extra gold. Using the Scouter Gear (20 trophies) will make this 250 per time, making this achievement very easy.

This achievement can be earned irrespective of your choice of character, and is not affected by diffculty, so you can play on Transcended Universe 0.

50 cards by the end of the game may sound like a lot, but its not as hard as it sounds. Each time you kill an enemy exactly (a 'Precision' battle tech), you will earn 50 gold (assuming no gear, the 'Scouter' gear will make this 250). If you are careful to do this as often as you can, you are very likely to reach an amount of money that will be sufficient to go for this achievement. Gold is also offered as a mission reward sometimes, and may be better than taking a single card (if you are using the Scouter, this is disabled).

There are 5 ways that you can obtain cards to add to your deck:

Starting Cards: No matter who you play as, or which deck you use, you will always begin your journey with 8 cards.

Random Bonus Before Game Start: Sometimes, if you made it far enough in the previous run, the AI will "use energy from a previous universe" and offer you bonuses before the run begins. These can sometimes be "Receive 1 of X Random [Rarity] [Type] Cards", which will grant you an extra card even before stage 1-1.

Battle Rewards: After (almost) each fight, as a reward, you will get a choice of three cards to add to your deck. On a high enough level of Transcended Universe, these may actually be Hindrance Cards that you don't want to add, though I have yet to see one with all three being these.

Mission Rewards: Each battle you take (apart from the last bosses) comes with an attached mission, that if you complete it's requirements, grants you a reward. If you want 50 cards, try and grab as many of them that reward new cards as you can, even when the other rewards are better. Needless to say, avoid missions that remove cards from your deck like the plague (though as long as you don't redeem them, you are fine if you take one by accident)

The Data Store: The shop of the game that will offer you six cards per refresh. Depending on card rarity and type, the price can vary between 60 gold and ~225. There are sometimes skills that will help you (one lowering item prices, the other the refresh cost, for a few skill points each. There is also a skill to just grant you 300 gold), it helps immensely if these spawn in your run. In my opinion, especially while refresh cost is low (it begins at 0, increasing by 50 each time, or 40 with the relevant skill, up to a maximum of 250/200), cards costing more than ~150 are not worth it, unless you actually want to use them specifically. The store may also offer 50% off cards sometimes, these are always worth grabbing.

This means that for 50 cards, you need to acquire 50 - (8+(1)+14) = 28(27) cards from missions and the store, over the first 14 stages. Try not to spend gold unless it is on cards or resetting the store, as you will need to buy a fair few to hit the target.