This is not difficult, just time-consuming.
Things that will help though are:
Complete the single-player story-line firstThe single-player campaign/story has a set of mandatory championships; completing it first will not only get you underway, it'll also ensure you don't complete any championships unnecessarily by making you redo them in the campaign.
Championship order and rotationMake sure you rotate locations of the championships you do. You must move from one championship location to another, so in order to ensure you don't end up having to redo championships because the one you need is in the same location you were just at, rotating is a must.
To minimise the travel time between championships, and maximise location rotation, I suggest doing them in this order:
1. Castelletto
2. Montellino
3. San Giovanni*
(end of road trip - journey to hub for the "Awards Party")
4. Nice Massena
5. Sisteron
6. San Martin
(end of road trip - journey to hub for the "Awards Party")
Start again at 1 and repeat.
*NOTE: when returning from San Giovanni to the hub for the "Awards Party", the sat nav gives you a crazy 14km route back. Ignore this! Instead, turn right out of the garage, and head towards the roundabout just down the road....once you get there, follow it straight on (continuing in the same direction - south), then follow the road along until you need to take a left to go under the motorway/freeway. Just before this left turn, the sat nav will update to just under 3km! Saves a lot of time over the 168 championships.
Do it in sessionsI suggest doing it in lots of 3...and at least 3 a session. This completes a road trip and doesn't take overly long.
Ignore suggested championshipsBe sure to always choose the championship you want to do rather than one from the suggested set. This means you're not going to do a repeat one, and also means you can get a set of championships done at the locations of your choosing.
Kill two birds with one stoneIt's a good idea to buy a new car each championship. This means you can do the
achievement more naturally and have a set of great cars for every occasion. it also adds a bit of variety (you'll have long-since exhausted all the radio stations by the end, and even tried Levante for more than five seconds!).
Do all championships at S2/X classI've not actually done this myself, but this would make things quicker if you so wish.
Best of luck! It's going to take time, but you'll get there!