Here is the full list of all 55 Road Redemption achievements. It takes around 20-25 hours to unlock all of the achievements on Windows.
Completed Campaign Plus Ten Times
Beat The Game With Felicia
Gold Trophy For Explosive Heat Quick Race
Gold Trophy For Desert Alliance Quick Race
Gold Trophy For Apocalypse Now Quick Race
Gold Trophy For Imminent Death Quick Race
Beat The Game With Elijah Price
Beat The Game With The Barbarian
Beat The Game With David Dunn
Beat The Game With Pumpkinhead
Beat The Game With Fredrick Sykes
Complete the game 20 times
Beat The Game With John Spartan
Beat The Game With Jack Traven
Completed Campaign Plus Five Times
Completed Campaign Plus Once
Win 1 MILLION Dollars over all playthroughs
Beat The Game With Santa
Beat The Game With Leonard Shelby
Complete the game 10 times
Beat The Game With Shovel Knight
88 Samurai Sword Kills
Reverse Achievement-Die 30 Times
Beat The Game With Nathan Algren
Defeat 50 Enemies with a Bat
40 Enemy Deflections
Beat The Game With Motosoldier
Complete the game 5 times
Gold Trophy For Phantom Wheels Quick Race
Gold Trophy For America's Ruins Quick Race
Gold Trophy For Danger Zone Quick Race
Gold Trophy For Ice The Cops Quick Race
Gold Trophy For Devil's Bridge Derby Quick Race
Gold Trophy For Ridge Rampage Quick Race
Gold Trophy For Rooftops Run Quick Race
Gold Trophy For Winter Support Quick Race
Gold Trophy For Boom Trucks Quick Race
Gold Trophy For Desert Dash Quick Race
Gold Trophy For Raging Plateaus Quick Race
Beat The Game With Nitro Punk
Beat The Game With Dutch
Beat The Game With Gordon Gekko
Complete the game 1 time
Get to the Full Spectrum Highway
20 Sledgehammer Kills
Kill 1000 enemies
100 Gun Kills
Reached America's Ruins
Reached the Devil's Cave
Reached the Winter Level
Reached the Rooftop Level
20 C4 Kills
Reached Ridge Rampage
Reached the Devil's Bridge
Reached the Raging Plateaus