Not the easiest of birds to expose correctly as with even with the dimmest of fill flash the blue colours may be blown especially under canopy cover in this case.
These Verditer Flycatchers are normally seen in pairs. Here's my take of this one from Bukit Tinggi in Pahang, Malaysia. Would have preferred the subject to have been lower but this was the best on the day.
1D MkIII + EF600mm + 1.4II ext
1/100s f/9.0 EV -2/3 iso400 Evaluative metering Fill flash -3
Like the blue color of the bird against a pretty green BG. Pose is less than ideal as you stated. I would try to selectively brighten the bird. Thanks for posting!