You just need the Atmel AVR 8-bit Toolchain. The latest should be fine, as of writing it was 3.4.3.
http://www.atmel.com/tools/atmelavrtoolchainforwindows.aspx
+(Atmel AVR 8-bit Toolchain 3.4.3 - Windows)
Extract the files to a directory, say C:\avr8-gnu-toolchain. Then copy all the folders in that directory to the Cygwin directory.
Mine is C:\cygwin64.