Web Master:
So no chemicals. Does that include vinegar?
If not then vinegar with a little salt and a dash of washing up liquid, sprayed on, being careful not to over soak the soil, aiming mainly at the leaves.
Nettles can be a bit aqua-phobic e.g. repels water, hence a little surfactant in the dishwashing liquid to break down surface tension.
The salt isn’t vital but it makes the mix more potent - but its important not to let too much salt collect in any one area of soil or it will not support growing plants for a while afterwards. If however this nettle patch is not intended for more plants, then you could increase the salt content, which will make your spray all the more effective.
Spray it on during mid morning of what will be a sunny, rain-free day for best results.
The only other solution is boiling water, though some say that a mix of acetic acid and clove oil also works well.