Here is the full list of all 49 Sprint Vector achievements.
Finish the Basic Tutorials
Get a Gold Medal in "Winter Rush"
Get a Gold Medal in "Aesir Village"
Get a Gold Medal in "Pharaoh's Scrapyard"
Get a Gold Medal in "Ra's Revenge"
Get a Gold Medal in "Toxic Barrage"
Get a Gold Medal in "Sludge Blitz"
Get a Gold Medal in "Castle Valhalla"
Get a Gold Medal in "Fimbul Tundra"
Get a Gold Medal in "Burning Necropolis"
Get a Gold Medal in "Edge of Amenti"
Get a Gold Medal in "Machine Death"
Get a Gold Medal in "Industrial Havoc"
Get Any Medal in "Winter Rush"
Get Any Medal in "Aesir Village"
Get Any Medal in "Pharaoh's Scrapyard"
Get Any Medal in "Ra's Revenge"
Get Any Medal in "Toxic Barrage"
Get Any Medal in "Sludge Blitz"
Get Any Medal in "Castle Valhalla"
Get Any Medal in "Fimbul Tundra"
Get Any Medal in "Burning Necropolis"
Get Any Medal in "Edge of Amenti"
Get Any Medal in "Machine Death"
Get Any Medal in "Industrial Havoc"
Get a Gold Medal in Any Race Map
Get a Gold Medal in All Race Maps
Get a Gold Medal in "The Premiere" Across All Modes
Get a Gold Medal in "Termination" Across All Modes
Get a Gold Medal in "Driftway" Across All Modes
Get a Gold Medal in "Trip Hop" Across All Modes
Get a Gold Medal in "Killer Boost" Across All Modes
Get a Gold Medal in "Precipice" Across All Modes
Get a Gold Medal in "Sidewinder" Across All Modes
Get a Gold Medal in "Blastoff" Across All Modes
Get a Gold Medal in "The Gauntlet" Across All Modes
Get a Gold Medal in All Challenge Levels for Time Trial Mode
Get a Gold Medal in All Challenge Levels for Collection Mode
Get a Gold Medal in All Challenge Levels for Hardcore Mode
Get a Gold Medal in All Challenge Levels Across all Modes
Finish the Intermediate Tutorials
Finish the Advanced Tutorials
Unlock All Racer Skins
Finish in First Place in an Online Race
Use the "Chronoshift" Power-Up
Blow Up an Opponent Racer's Mine
Destroy 50 Breakable Objects
Use an Impulse Shot to Eliminate an Opponent Racer
Use a Crash Missile to Eliminate an Opponent Racer