You can upgrade your bikes by selecting "Garage" from the main menu and then choosing the "Bike Upgrade" option. Upgrades are available in multiple categories, covering:
- Engine (top speed)
- Gears (acceleration)
- Tyres (handling)
- Shocks (tricks)
- Paint job (cosmetic)
Highlight your chosen category and press right on the D-pad to navigate through available options. If you do not have any items available to buy, or do not have enough money, complete events (make sure to grab coins, too) to unlock items.
Personally, I did the first Exploration level and collected enough skulls to earn a bronze medal. This unlocked several items, and due to my coin collecting, I also had enough to buy several upgrades.
The achievement will pop as soon as you buy your first upgrade of any kind.