NOT a max build:
max build in Road/Race:
Pay attention to where the dot on that graph is located in order to setup your car for any of the 4 particular achievements. The ONLY parts that affect this handling graph are SUSPENSION & TIRES under the chassis category and DIFFERENTIAL under the drivetrain category. MOST exotic/sports cars in the game can achieve "max" handling in all categories with the exception of OFF-ROAD. So to put things simple just adjust the 3 parts I listed until the car reaches max in the desired category. For your off-road achievement I'd suggest grabbing a truck or SUV of some kind due to many cars being not able to achieve max off-road even with the best part rarities & yes rarity DOES matter.
Lastly, go and WIN a race with your new "max" vehicle in your desired category. I can also confirm that drift trials count as a race.