When a unsuspecting son of the leader of a death squad discovers that blood thirsty aliens are hunting his family, he has 1000 hours to get to Bolivia, and close the gateway before Earth is bathed in blood..

It is a little wordy.

I think you should choose another adjective to describe the son as it is apparent he would be unsuspecting bloody thirsty aliens to hunt his family.

Also it's not quite clear- I first read it that the aliens are going to kill everybody in the whole earth.

Why does he have to go to Bolivia? Not sure it is necessary to the logline to mention Bolivia. Could it be referred to more in general terms- eg home?