Always get Chronos. When Grover roots you with cripple, put up your shield, then rocket boots away. Loadout that allows turrets to heal you can also be useful.

Go up close to Grover when fighting him 1v1. You deal more damage to closer enemies, Grover does less damage to close enemies. Don't forget to place turrets; it grants you extra bonus damage.

Don't attack Grover when he ults. Reload your ammo, and wait your abilities to cooldown. His healing is more than the damage you can deal.