Pokémon GO Team Rocket Leader Counters is important to know if you want to take down Giovanni and save Entei. Giovanni will have a different Legendary Shadow Pokémon each month, and his team changes as well so this guide is good for February 2020.
Pokémon GO Team Rocket Leader Counters: How to Beat Giovanni
The first Pokémon Giovanni sends out will always be his signature Persian, no matter when you fight him. Persian is just Normal type, so it is only weak to Fighting type moves. Persian can learn Fairy type moves to cover Fighting type Pokémon, so any high defense Pokémon that can resist Normal, Dark, Rock and Fairy moves will be good here. Melmetal and Registeel can both learn Fighting moves and resist Persian's attacks. Lucario is also a good choice.
Giovanni's second Pokémon will either be Kingler, Steelix or Rhyperior. Steelix and Rhyperior are weak to Water type moves, and Kingler and Rhyperior share a Grass weakness.
Bring a strong Grass type like Torterra or Venusaur to cover Kingler or Rhyperior. In the case of Steelix, your third slot should be Water type Pokémon, as it will cover Giovanni's last Pokémon.
Shadow Entei is the last Pokémon Giovanni will send at you, and it's just pure Fire type. Swampert or even Kyogre will be able to make short work of Entei, as it can use Steel type moves that Water resists.
Defeating Giovanni will give you the chance to catch and purify Entei.