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