What I did was use the small boxes to get up on top of the big ones, sprint jump to the edge of the first platform, and walk around the big box between you and the rat (slowly, otherwise you'll fall off)
it doesn't make any sense. I simply not able to jump high enough to get on top of those boxes at the top-left corner of the room. Sprint doesn't make difference. Tried to use some small object like that teddy bear to give me just a few pixels, however, still no luck.
