You have to "win" or get three stamps on every single event for this. All of these events (With the exception of one) are easy to complete as long as you have the difficulty set to very easy.
There's a Smash Attack event that is required for this. This will just simply take a few attempts to do as you find out a route that works best for you. It's not really that hard, but here is the route that got me 4500 exactly in about 1:36.
This should get you exactly 4500. If it didn't, make sure you're collecting every single one along this path. (or if you see one that you don't have to go out of the way for, get that too.) it will take a few tries but you will get it eventually.
For the last sprint event in the dlc, it's mandatory that you use the sprint car that used to control terribly. It seems like they definitely fixed the handling on this, as it actually worked the way it should for me on very easy difficulty. Even if I hit the wall, it didn't stop me for long and I was able to get first by quite a bit.