Uses objdump -x and looks for DLL Name: lines. i.e:
 0objdump -x src/qt/bitcoin-qt.exe | grep "DLL Name:"
 1	DLL Name: ADVAPI32.dll
 2	DLL Name: dwmapi.dll
 3	DLL Name: GDI32.dll
 4	DLL Name: IMM32.dll
 5	DLL Name: IPHLPAPI.DLL
 6	DLL Name: KERNEL32.dll
 7	DLL Name: msvcrt.dll
 8	DLL Name: ole32.dll
 9	DLL Name: OLEAUT32.dll
10	DLL Name: SHELL32.dll
11	DLL Name: SHLWAPI.dll
12	DLL Name: USER32.dll
13	DLL Name: UxTheme.dll
14	DLL Name: VERSION.dll
15	DLL Name: WINMM.dll
16	DLL Name: WS2_32.dll