There are a lot of different species of prickly plants around the country that are called briars.

Can you identify your exact plant species? (There may be a noxious weed department in your county that could help with the identification and make an expert treatment recommendation.)

I have some invasive plants that are relatively easy to control by foliar spraying (spraying the leaves and stems). However, this type of treatment will almost certainly result in some overspray going into your pond.

Some plants are very difficult to control - even when you soak the leaves with a powerful herbicide. For these plants you are much better off using a "cut stem" treatment. This is more work, but if that is the recommended treatment for your type of briars, then it will be much more effective AND keep the herbicide out of your pond.

If possible, whack the plants off clean at whatever height is easiest for you. (Use a machete, heavy weed trimmer, loppers, as you determine which is easiest.) Do about 10 plants then apply poison. Some plants are amazingly quick at sealing up their vascular systems.

For some of my herbicides, I like a mason jar and a paintbrush. Brush a thick layer of poison on the fresh cut, then stick the brush in a 7-11 cup, seal the mason jar and drive over to the next briar location. This method will not get herbicide in your pond.

EXCEPTIONS
There are a few "systemic" herbicides that can work down from a plant's surface foliage, then into the roots, then into the groundwater in the soil. These COULD work into your pond. However, these herbicides are not typically available at your "big box" hardware stores.

Good luck fighting your briars!