There were some changes to how the executable links work in recent versions of Cygwin. The latest version of jGRASP should handle those, so you probably need to upgrade . Then you won't need a custom compiler environment as your instructor suggests, just go back to the default.
Also, make sure you actually have the g++ compiler installed with Cygwin (install "All" with Cygwin if you have the space).
If that doesn't help, turn on "Settings" / "Verbose Messages" and send a bug report using "Help" / "Report a Bug" that includes all of the output from a failed compile.