This is not as difficult as it first appears and is easier if you get your tactics right during the whole season.
You have to remember if you take on a rival and win he will miss 2 races when you are driving his car, so even if he has a slight lead in the championship you have 2 free races to make points back on him.
In my season I started with Caterham and choose Paul Diresta as my first rival, beat him and chose Felipa Massa as my second, beat him and chose Sebastian Vettel as my third, beat him and chose Lewis Hamilton as my fourth, I beat him and the achievement popped although there were still 2 races remaining no one could catch me.
I chose Vettel and Hamilton because at the time they were closet to me in the
standings, yours will be different and you should choose carefully.
Also another point on Season Challenge is don’t be afraid to push and shove other cars, it seems to be easier getting away with contact, and flags don’t seem to be as strict for some reason, blocking a lot seems to be fine if you can manage to get yourself up near the front of the field.
If you are being over taken it will generally be people at the top of points, so another trick is at the last second block them and they will have to brake hard and this may force them to drop back a few places allowing you to get more points than them, also another tip if you are in top 3 in the race brake hard on last corner and block as much as you can so the others all bunch up letting the slower drivers potentially past them.
If you get caught for any contact or blocking then remember to use your flashbacks.