There are 5 new cars, and each car has 5 events. Unlike Second is Nothing (achievement from the main game), this achievement isn't unlocked by winning just once in each unique event. Placing first in all 5 events using all 5 cars is required to unlock this achievement. (25 events total)
The events consist of a mix of races and speed runs. The majority are new (indicated by a red icon in the Easy Drive menu), with a couple of old events borrowed from the main game. Start with the easier events and unlock mods to make the higher difficulty events easier.
4 out of the 5 cars are, along with all their Jack Spots, are available as soon as the pack has been purchased. The Hennesey Venom GT Spyder is unlocked by winning the "Most Wanted Venom" event and shutting them down after the race.
The new cars in the Ultimate Speed Pack:
Pagani Zonda R
Bugatti Veyron Grand Sport Vitesse
Lamborghini Aventador J
Mclaren F1 LM
Hennessey Venom GT Spyder
Note: If you have downloaded any of the newer DLC Packs (Terminal Velocity, Movie Legends, NFS Heroes) you may see up to 3 additional events. The additional events unlock Ram Chassis, Drift Tires, and Jump Nitrous. These events are not required for the achievement.