It seems 24 before.
But there are only 22 cards in my game, and I got the achievement after getting the 22nd — the last cards (it's No.22 by coincidence).

After completing every level on normal & fully upgraded my plane, I got about 6 cards. then my next aim is to collect the rest.
6/22

At first, it feels terrible, I can't get cards anyway. But I made some research and probably got the point, finally collected all cards. I think it is the hardest achievement. Here's my experience:
(Thanks to All of You guys)

I tried every level on every difficulty but only received tiny effects...
Then suddenly I got about a dozen of cards on Lv6 insane, continuously. (always a card almost every single run! )
15/22

After that, drop rate seems been decreased somehow. But I still got one card the same level in three or four runs on average, then card seems never drop anymore.
18/22

Next day, I started the game and got two cards on Lv7 insane in very first four runs, then nothing again.
20/22

Two days later, several runs on Lv8 & 9 insane (died midway) but find no card, then three runs on Lv7 insane and got the last two cards:)
22/22


I found some interesting code in registry
poll_level6_hxxxxxx 1023
poll_level7_hxxxxxx 107734
poll_level8_hxxxxxx 55631
Don't know what they mean. Drop rate? Or maybe nothing.

So here's my conclusion:

Surely you can get all cards without farming on Lv8 or Lv9.
Surely you can get all cards without getting all 108 medals. ( I had only 102/108 medals at the time I collected all cards. Lv8 with 10 medals and Lv9 with 8. )
Yes, it drops more often on higher levels on insane difficulty.
Lv6 and Lv7 are the best choices (many boxes and not hard to survive).

Fully upgrade your plane, because you will get a card only if you grap it and complete the level alive!

Maybe more medals cause more drops?
I recommend you to earn many medals first ( There's still the 100 medals' achievement to go anyway. )
Maybe more cards you lack, more often they drop.
Maybe you can't get cards endlessly in a period of time? Take a break and try later.

Hope it will be helpful to you:)

Originally posted by kerberos_20:

u can get all cards even on high diffculty, but wth every start u fnsh level, chance for car drop decreases...so make sure u playn on level wth only 1 star completed at max and cards will drop like every second level