Cards are an item that can be found in the wooden crates that are skattered throughout the levels. Once collected, the player MUST complete the level for the card to unlock. It appears that card drops from the crates are more common the higher the difficulty that you choose, as well as the level you choose.
Cards give passive effects to your ship. For anyone Curious, here is an image of all of the effects:
A short preface to the guide: Difficulties in this game can be unlocked by obtaining all of the medals in the previous difficulty. This works up to Insane difficulty (Normal > Hard > Insane) until you complete level 8 which will allow access to Nightmare difficulty (provided you have all medals on insane).
OK, now onto the real guide. I found that Level 8 on insane difficulty was a very good level to grind for all of the cards. I would suggest Nightmare on level 8 if you are able to clear 100% of the enemies on insane, but i found that they have way too much health to manage this for myself.
Start the level by buying 4 shields, 4 lasers and 2 bombs which will cost around 3,250 Stars (slightly less if you have cards that provide an initial shield, laser or bomb). The cost of grinding this level will not be an issue however, since you will obtain approximately 2,500 to 3,000 Stars per run, which will double to 5,000 to 6,000 Stars per run once you unlock the double star card.
It is also worth continuing the level even if you don't find a card, since you will still need stars for the 500,000 star achievement anyway.
If level 8 isn't your style, i found that Level 6 or 7 on Nightmare difficulty also gave a fairly good chance of a card. The setup for these levels is exactly the same in terms of what to buy, just remember to save shield/lasers/bombs for the boss if you choose level 7 because it can be a pain to kill without them, especially on nightmare.