Here is the full list of all 53 Dark Rose Valkyrie trophies - there are 45 bronze, 5 silver, 2 gold and 1 platinum.
Achieved the True Ending on [Very Hard].
Used over 100 Special Skills.
Inflicted over 500,000 damage during battle.
Cleared the game.
Developed over 100 Remodeling parts.
During the eleventh eradication mission, eliminated all Chimera.
Defeated Shadowrise Kaiser during the fourth Dangerous Creature extermination mission.
Defeated Anoma Shadow during the third Dangerous Creature extermination mission.
Strengthened any TCS to its maximum.
During the tenth eradication mission, eliminated all Chimera.
Defeated Balt Kaiser during the second Dangerous Creature extermination mission.
During the eighth eradication mission, eliminated all Chimera.
During the seventh eradication mission, eliminated all Chimera.
Defeated Barakeet during the first Dangerous Creature extermination mission.
Used over 100 Cooperation Attacks.
Used a Special Skill for the first time.
Used Support Defense over 50 times.
Inflicted over 100,000 damage during battle.
Defeated 1000 Chimera.
During the sixth eradication mission, eliminated all Chimera.
Defeated Jormurgand during the third night extermination mission.
During the fourth eradication mission, eliminated all Chimera.
Used over 100 Side Attacks.
During the third eradication mission, eliminated all Chimera.
Used over 100 Additional Attacks.
During the second eradication mission, eliminated all Chimera.
Used Overdrive for the first time.
Used a Cooperation Attack for the first time.
During the first eradication mission, eliminated all Chimera.
Defeated 100 Chimera.
Number of HITs during battle passed 300.
Number of HITs during battle passed 200.
Repaired a uniform for the first time.
Used the Treatment Room for the first time.
Used Ignition for the first time.
Developed a Remodeling part for the first time.
Changed your formation for the first time.
Used Support Defense for the first time.
Number of HITs during battle passed 100.
Inflicted over 10,000 damage during battle.
Used an Additional Attack for the first time.
Used a Side Attack for the first time.
Defeated a Chimera for the first time.
Obtained all trophies.
During the twelfth - fifteenth eradication missions, eliminated all Chimera.
Defeated Ignis Dragon during the ninth elimination mission.
Defeated Gigant Armor during the fifth Dangerous Creature extermination mission
Defeated Chimera-Anima during the sixth Dangerous Creature extermination mission.
Defeated Roblebraun during the seventh Dangerous Creature extermination mission.
Defeated 10000 Chimera.
Strengthened any uniform to its maximum.
Raised any stats to 999.
Cleared the eighth Dangerous Creature extermination.