Win (or at least finish) every single event in the game with every single car used by AI opponents. It has to be exactly like the cars right down to the tires and oil. So if the AIs in the 4WD championship use a Dodge Ram modified in a certain way and running on Comfort Soft tires, you have to win every race of the 4WD championship in a Ram with the exact same modifications and tires.
Extra difficulty mode: Do it with the special events too.
Super difficulty mode: Do it in B-Spec too where possible.
Mega difficulty mode: Then come back and do it in A-Spec with cars not used by the AIs but still appropriate to the event (modify if you have too. Some kind of spreadsheet may be helpful here.)
Epic difficulty mode: Do that in B-Spec too.
Excessive difficulty mode: Do that in every single GT game you have (excluding B-spec of course). Tire compounds can be switched in GT4 as long as you use the same type of tires the AIs use.
You'll never finish it mode: Write race reports on every single race and post them here.
You'll really never finish it mode: Do it in NFS Shift and Shift 2 (at least the endurances). And write reports on it.
This is your life mode: Continue this pattern with other racing games such as Grand Prix Legends, Enthusia, etc etc until you realize you never do anything except play video games.
You have no life mode: Do all of the above while actively participating in online league races for all applicable games.