How much Accuracy do I need to hit Athena Pierce's Clone at a high rate?

At lv 70 (which I assume you will be when you fight her ), you need 127 acc for 100%, which you shouldn't hope for I guess. So you could settle for 110-120 which will give you 73-88%.

Yes, as an Archer, you should cap your DEX at 200.

The only problem will be the possibility of her killing you. As long as you don't die, it'll be easy, and if you can snipe at her from the top of the hill while she's down the slope, you won't take damage until she summons.