The chaos archer patrols between bandit copper mine and logging camp in farbane woods, and using terrain is your best chance here. Keep an eye out for natural cover like rocks or trees when she starts her chaos arrow barrage, because that burn effect is brutal if it connects. The main thing to watch for is her 3-shot volley and that nasty 4-shot ground attack, which you'll know is coming when she shouts about stink on your feet

Clear out the regular enemies first along her path, trust me on this one. When she goes invisible try to force her into tight spots between terrain features, makes her way more predictable. Your best setup is gonna be copper sword with gravedigger ring and nightstalker gear, gives you the defense and mobility you need

Tip: those chaos arrows leave fire on the ground that sticks around for a while so always keep an escape route in mind. When you take her down you'll unlock 1 tier I chaos point and the devourer bench, which makes the whole fight worth the trouble. Blood rage and dash abilities are really helpful here, especially when you need to get behind cover fast or close distance for damage windows

Remember to watch her patrol route and set up your ambush point near some good cover, way better than chasing her around in the open