Uses objdump -x and looks for DLL Name: lines. i.e:
objdump -x src/qt/bitcoin-qt.exe | grep "DLL Name:"
DLL Name: ADVAPI32.dll
DLL Name: dwmapi.dll
DLL Name: GDI32.dll
DLL Name: IMM32.dll
DLL Name: IPHLPAPI.DLL
DLL Name: KERNEL32.dll
DLL Name: msvcrt.dll
DLL Name: ole32.dll
DLL Name: OLEAUT32.dll
DLL Name: SHELL32.dll
DLL Name: SHLWAPI.dll
DLL Name: USER32.dll
DLL Name: UxTheme.dll
DLL Name: VERSION.dll
DLL Name: WINMM.dll
DLL Name: WS2_32.dll