Virgin Trigger

One day a girl appears from the window. She asks main character to fight together to protect the Earth. She starts to train together with protagonist until the day of decisive battle.

[From vndbreview]

Aliens fight a proxy war for control of planets by creating "triggers" who must do battle with each other. They are androids with human hearts. Haruka is a trigger girl that the protagonist must train to be ready to defend the earth. The final battle will be determined based on how you have trained and treated her.