Feral Fury (UP)

In order to upgrade you need orbs, which are collected in game by killing things and are cross game collectibles, meaning it doesn't matter what difficulty you're on or if you die you always get to keep the orbs you collected.
On the main menu go to "Upgrade" and from there you can upgrade whatever you wish, I recommend doing the 2 Health related ones first, then maybe ammo.
After every playthrough; whether its a successful one or not I recommend upgrading whatever you can afford at the time.