Honestly, I feel like Ivy was a lightweight in Battle Ground. In the Shed Aquarium battle, she fought many Denarians at once, but in Bettle Ground, she had "heavy things" floating around her. It doesn't make sense to me why if she was so skillful, she would use blunt objects as her weapon of choice. Why not a fistful of Mordite or lightning or some other more elemental or powerful weapon. While Ivy has a large magical "battery" and is very talented in some aspects, I think her human side prevents her from becoming the ultimate powerhouse she could become. Maybe as she ages, she'll learn how to use her power in other ways.
Update/edit:
On the other hand, maybe my thinking is wrong. When I was writing this, I was thinking of physical power. However, that's not what the Archive is supposed to be. While the Archive can defend itself, its main purpose and power come from knowledge. So in incidences of mass casualty (such as post Battle Ground), she can direct humanity in the most efficient ways possible and can preserve knowledge.