This is written with respect to Card Expert, but the suggestions are the same.MAJOR CAVEAT:
Not all cards are available at any time. A large number of cards are moving in and out of circulation, so 400 will likely not be available all at once for a long time, if ever. In any case, it's best to work toward new cards whenever possible.
The best ways to earn cards are to level up, move through the campaign and attack towers.
In the campaign, you can win specific cards for beating particular levels with certain conditions, such as playing with no runes, or with a certain number of cards from a particular type (Kingdom, Hell, Forest, Wilderness). You can also win scraps of cards by exploring certain levels after completing all stars on a map.
The walkthrough lists all of the card you can win through normal campaign play. I've found it helpful to list all of the cards and scraps by location, in order to find out which cards I will earn through normal campaign progression, so that I don't waste universal scraps composing a card for my collection that I won't really need.
Below, in the spoiler, is the list of all 3-star, 4-star, and 5-star cards available through the campaign, in alphabetical order. This is so that if you're looking for a particular card, you can find it more easily. 1-star and 2-stars drop easily as you progress, so you should easily earn all of these except for special event cards.
Quite a few cards can be found in towers, especially the Mystery Tower, which drops no less than a 3-star card at every drop, making it a good place to try to win the rarer cards.
The Mystery Tower only opens once you have opened the Sky Tower in the 8th world. Then you are given the opportunity (under Mission) to clear all 7 towers again. Once you do this, the Mystery Tower is open for TWO HOURS after the 7th tower is cleared. Towers may be cleared once per day, so generally you will be able to access the Mystery Tower only once a day. Note that in order to clear the towers, you will need at least two full charges unless you choose to buy energy (not recommended).
Dungeons also help you earn cards when you can reach the later levels, but these are usually scraps to build cards.
Events also give you the opportunity to win new cards, but these are harder to earn for free.
In short, there are just over 400 cards, so you have to have a high enough level to clear the Mystery Tower on a regular basis, and also be very lucky. Those who complete this in the very near future will have incredibly high levels, although over time (unless new achievements are added, which may very well happen) you should be able to earn cards more easily as new cards are added.
This will take a lot of dedication over a very long period of time. Build strong decks, level up for more HP, and keep attacking the towers. Best of luck!
Hope this helps!