Bulldozer will be your best friend. Anything that cripples as she get low on HP is almost necessary. CC reduction is also gonna be a big difference. Take out her foxes first enemies second, her healing is very solid so focus on her not the tank.
If you find IO while Luna is still active, instead of targeting Luna to get her down go for IO. When she dies, her fox dies. This is similar to Barik with his deployable and Inara with warder's field. They all are removed from the field after death