What's the best way to secure soffit that joins a roofline?
It's hard to say much from the very distant photo, but I'd guess that there's no metal channel against the roofing (shingles). That would prevent all but the burliest of birds and rodents from shimmying under. 

The wall has a channel for the soffit to slip into, and that channel should wrap down the slope to the backside of the fascia. 

Or, work in some lumber, fastened at the wall and fascia, to stiffen things. Don't puncture any existing roofing.