An emulator cannot function properly without this firmware because it needs to emulate the exact environment of a real PS2.
If PCSX2 says "BIOS image is corrupted or missing," the Internet Archive link contained a bad dump. You need to search for a different "Rev 2" or "Verified" pack.
When looking through a BIOS pack on the Internet Archive, you will see files labeled with different "SCPH" numbers and regions. It is helpful to understand what these mean:
Open your emulator, navigate to Settings > BIOS , and select the path to your folder.