The solution of Edward Hyena is absolutly correct, but there are some things you have to remember. Two of the offline cards are pretty difficult to achieve. 1. Getting $1.000.000 and 2. 20 Defense races.
For the $1.000.000, please check this solution:
You still can get the money after beating the story, but it will be annoying, since you only get about $500 per win by replaying older races.
For the 20 Defense races, please note: YOU MUST DO THIS BEFORE BEATING THE STORY. You will NOT be able to do these kinds of races after the story, because no rival crew is going to challenge you again. If you want to be challenged, play a race you haven't won yet, but lose it. I prefer Checkpoint Race, because you drive alone in case your teammate screws things up and wins. When you have the 20 races, you're free to beat the story.
EDIT: I heard a few questions about these defense races, mostly because they won't pop up. If that happens to you, try the following: Play a few races (around 4 or 5 is sufficient) that you ALREADY WON! Now, play a race you haven't won, try to win it and with a little bit of luck, a rival gang challenges you to a Defense Race. I hope that helps.
As for other cards, leave me comment or write me a message and I will help you out. Any card but these two can be achieved even after the story or in Quick Races.
Good luck with that achievement!