From The TimeSplitters Wiki

The fists are you last resort, for when you've run out of all other options. Surprisingly, the fists can be very powerful. You'll always have them with you no matter what.

Tips

The best place to aim for when using fists on an enemy is the back of the head. If you can get up behind them while they're fighting someone else, you can kill them before they even see you. However, if they do see you, you should keep attacking and moving randomly, but staying as close as you can. This will make you much harder to hit with most guns and you shouldn't have too much trouble evading.