Here is the full list of all 25 Azure Striker Gunvolt achievements.
Obtain a S+ Rank on the 1st Sumeragi Stage
Obtain a S+ Rank on the Subaquatic Base Stage
Obtain a S+ Rank on the Media Tower Stage
Obtain a S+ Rank on the Biochem Plant Stage
Obtain a S+ Rank on the Datastore Stage
Obtain a S+ Rank on the Stratacombs Stage
Obtain a S+ Rank on the Pharma Lab Stage
Obtain a S+ Rank on the Sinner's Row Stage
Obtain a S+ Rank on the Urban Run Stage
Obtain a S+ Rank on the Eridu Stage
Obtain a S+ Rank on the Babel Stage
Obtain a S+ Rank on the Firmament Stage
Obtain S+ Ranks on all of the Special Stages
Complete all the Challenges in the game
Complete all of the Achievements
Clear a stage without taking damage
Acquire all of the weapons in the game
Learn all of the skills in the game
View the Normal Ending of the game
View the True Ending of the game
Use over 100,000,000kw worth of electricity
Move a total distance of 42 kilometers
Talk with Joule 10 times
Listen to all of the songs in the game
View the “Creepy Electro-whip Guy” sequence.