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1. Battleship
2. Battle Los Angeles
3. Chitauri
4. Skyline
5. Mars Attacks
6. Spielberg War of The Worlds
7. Independence Day
8. GORT

Bloodlusted; no PIS/CIS
How low do the Project Monarch monsters go?

You have wrong that list, put the Chitauri first, they are the most pathetic alien invasions in that list.
That said, Godzilla and co stop at Independence day aliens.

Could stop at war of worlds...depends on if Godzilla can breach the tripods shields. Not sure if tripods disintegration rays would hurt godzilla thougjh.