What is the meaning of "damnedest "?

A moment of sobriety arrives as I stand in the doorway, hand on my throbbing hip, trying my damnedest to not look as drunk as I truly am. “Maybe you’re right. Maybe it is best if you leave in the morning.”
Having spoken coherently, drunkenness again crashes over me. I sway out of the room, needing multiple attempts to close the door behind me. Then it’s into my own room, where more wrangling with a door ensues.
Jeff is half-awake when I flop into bed, murmuring, “I heard shouting.”