Here is the full list of all 22 Blade-Shift Rage achievements.
Finish the training stage
Finish sunset city stage
Finish subway stage
Finish skyline stage
Finish escape stage
Finish freight train stage
Finish neon stage
Finish mansion stage
Finish the story
Achieve an S Rank in the training mission
Achieve an S Rank in the sunset
Achieve an S Rank in the subway
Achieve an S Rank in the city
Achieve an S Rank during the escape
Achieve an S Rank on the train
Achieve an S Rank in the Neon lights
Achieve an S Rank in the Mansion
Achieve an S Rank in the Lab
Perform a 5X combo
Perform a 10X combo
Perform a 15X combo
Perform a 20X combo