Here is the full list of all 19 Risk System achievements.
Ending B
Attain a combo multiplier of 128
Achieve Rank S on Mission 1
Achieve Rank S on Mission 2
Achieve Rank S on Mission 3
Achieve Rank S on Mission 4
Achieve Rank S on Mission 5
Achieve Rank S on Mission 6
Ending A
Ending A All S Rank
Attain a combo multiplier of 256
Attain a combo multiplier of 512
Hit Ashley with the barrier breaker before the fight starts.
Achieve S Rank on the Trophaeum
Achieve A Rank on the Trophaeum
Achieve B Rank on the Trophaeum