Here's how I do it (link contains spoilers for this quest) :
- Persuade Kagha not to kill Arabella (several options based on different skill checks work)
- Snoop around in the Emerald Grove where Kagha is, there is a letter starting the "Investigate Kagha" quest (
wiki) regarding Shadow Druids (in a locked chest, behind bookcases).
- Go investigate the swamp, you need to explore the bog and to execute a jump to access the area.
- Go talk to Kagha (try to convince her)
TIP :
Successfully studying the fresco of Emerald Grove would help for the last step

but several dialogue options work, as long as you trying to stir Kagha to be on your side.