Encountering Grover in long range open spaces - don't PEEK around the corner.
Good Grover players throw axes preemptively and you can take a lot of damage. Use short sprints between cover. This way it's harder to predict where to aim.
Your ult is arguably worth much less than vivians ult in the long run, so letting her keep the drones up is a bad idea. If you have your ult when you hear her pull out her drones, seek her out and use your ultimate to kill her and her drones quickly.
If the tip of his arrow shimmers, he is preparing an Impaler Arrow. Avoid being pinned to the wall at all costs; his Planted will do 2400 damage before you can even move again, and likely another 2400 to follow, killing anyone.