Gryffindor:

Avatar of the Extinction (the apocalypse)- they would want to be part of ushering in a new, 'better' world

Fears the Slaughter (mindless violence)- pure, mindless violence is the opposite of honor and virtue, and they fear accidentally falling into it

Ravenclaw:

Avatar of the Beholding (constant watching)- they want to know everything and are willing to stand by and watch even if others get hurt, just to see what happens

Fears the Dark (the unknown)- the deliberate obscuring of information, combined with the dangers that may be lurking and unseen, are unbearable

Hufflepuff:

Avatar of the End (the inevitability of death)- they are patient and do not value anyone over anyone else, they know death comes for everyone eventually

Fears the Lonely (isolation)- being on the outside, unconnected to anyone around them, and knowing that they're not wanted, is horrifying to them

Slytherin:

Avatar of the Web (control)- they would like to manipulate situations so that they come out on top, and don't look suspicious getting there

Fears the Hunt (endless pursuit)- constantly chasing something and always being close without ever being able to reach it is a nightmare for ambitious people