Maximise screen brightness, go into Settings --> Display --> Background Effect --> Dynamic. That'll be the most you can do I would think. Note that the video player and camera viewfinder have their own outdoor visibility settings also.
Easiest way to change screen brightness is to turn off automatic screen brightness in display settings, then long press the notification area and wipe your finger from left to right to increase brightness (and vice versa). I make use of it quite a bit to quickly change screen brightness, since automatic changes never seem to be exactly what you want.