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.
Immortal will protect both you and nearby teammates from Drogoz's Dragon Punch. Wait until Drogoz finishes declaring his fury, however, or Immortal may end before he reaches you.
Unless your Champion's basic attack is hitscan, like Viktor or Tyra, you'll be hard-pressed to hit Androxus while he's airborne. Wait for him to land, if you can.