So I’m trying to find an anime film where humanity is on the brink of destruction by giant alien/monsters. Humanity fights these creatures with giant robots. The only other details I can remember is the protagonist’s father runs the brigade of robots and is just a terrible guy and the protagonist’s love interest dies and at the end of the film he says screw it and ends the world.
Quite probably Neon Genesis Evangelion:
The protagonist is Shinji, a teenage boy who was recruited by his father to the shadowy organization Nerv to pilot a giant bio-machine mecha called an "Evangelion" into combat with alien beings called "Angels".
(From the Wikipedia article)
It's a TV series, not a film, but spawned into a franchise that included several feature films (animated, with a live action long planned but never made) that apparently followed the plot of the series.
The "end the world" thing suggest that what you have seen was indeed one of the films, the aptly named "End Of Evangelion"
Concluding that NERV's defeat is inevitable, Gendo [Ikari, father to Shinji Ikari] retrieves Evangelion pilot Rei Ayanami. He plans to use her to initiate Third Impact, a cataclysm which will kill everyone on Earth [...]
(So it's the father who wants to end the world).