For ios9 Twitter integration using Fabric is working fine but when I am doing it for ios8 its showing all the 3 error
1) Could not build module 'TwitterKit'
2) Could not build module 'TwitterCore'
3) Cocoa/Cocoa.h' file not found
Try setting deployment target to iOS 8 (for project and target)in xcode 7 or above.I faced similar problem when i tried building using xcode 6.3.Also you can't iOS 7 as deployment target as TwitterCore doesn't support for iOS 7.Hope it helps :)
Edit
setting deployment target for project
For setting deployment target for target
I have used xcode 7.2 for running on device.It doesn't give any error.