I'm not experienced enough to put in a section about this, but maybe someone will one day.
(Originally posted on the game's steam community forum. View this post: https://steamcommunity.com/app/46560/discussions/0/1843493219427746731)
Computer\HKEY_CURRENT_USER\Software\Microsoft\Windows NT\CurrentVersion\AppCompatFlags\Layers
(not really necessary if you only have one user account) Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\AppCompatFlags\Layers
Look for: c:\gog games\robin hood - the legend of sherwood\game.exe
Double click it and paste this: DWM8And16BitMitigation 8And16BitAggregateBlts HIGHDPIAWARE RUNASADMIN HIGHDPIAWARE
The important one is 8And16BitAggregateBlts, this stops the lag, and you can't set this yourself in Compatibility tab.
This also works for Desperados before the modern system update, without the use of any DDraw wrappers, and it fixes all the problems:
-mouse cursor lag
-slow mission loading time, before 20s, now 7s
-slow gameplay, 1-10 FPS
-black traces on mouse path