This month's Legendary Shadow Pokémon that Giovanni has with him is and that we can capture after defeating him is Raikou ! Even though I made good progress January's quest throughout the end of January and the start of February I was struggling really hard to find Giovanni. One day he was at a Pokéstop in the city center that I heard from a friend, but it was such bad weather and I didn't have much time to play that day so I couldn't really attempt to defeat him. After that, and before that, whenever I'd be at a Pokéstop with potential to be Giovanni it was just a Decoy Grunt.
So I was pretty unlucky when it came to finding Giovanni this month even with getting to the quest step early. One good thing about encountering so many Decoy Grunts was that I could often get some extra Mysterious Components to build another Rocket Radar to use in fighting Team GO Rocket Leader Sierra a few times this month. She has a Shadow Beldum which has the potential to be Shiny. That's why I currently use the radar to fight her whenever I have one and can find her. And also to have a chance to get another great IV Beldum as they don't spawn that often around her.
Then just recently while walking around there were a few potential Giovanni Rocket stops that I was able to see with the Super Radar. So I was hoping I would be able to find Giovanni this time, at the first Pokéstop with one I was in no luck as it was yet another Decoy Grunt. After defeating it I decided to go to the one near the swimming pool to check it out, which was also a Decoy. From there I was able to see another local park / playground which has 4 Pokéstops and it showed a Giovanni stop as well. I don't go to that place so often, but I decided to continue walking there to see.
I was in luck, as Giovanni himself was at that the Pokéstop ! Finally my time had come to fight him and try defeating him to free the Shadow Raikou.
Against Giovanni I start out with my Lucario against him as Lucario is great at breaking the two shields and it's also super effective against his Persian. However his Persian seemed much stronger than last time as it was dealing so much damage to my Lucario even though it shouldn't have a super effective fast attack. Perhaps Giovanni's Persian can have another move that it can't usually have, or it just had a stronger fast attack than last time. My Lucario could just not properly survive against it and I was found to having to change my plan around. I did continue fighting to figure out what his 2nd Pokémon would be so that I could prepare my team against him for the next round. Which turned out to be Steelix.
For the second round I decided to start off with my Metagross. I knew it would also be taking a lot of damage from his Persian just like my Lucario, but Metagross' main goal here would be to damage Persian a bit and break one or two shields. I was able to break one shield as my Metagross fainted just before it was able to use its Meteor Mash a second time. Then came the time for my Lucario to start shining, as I switched it in to take care of Persian's remaining health and break his second shield with Power-Up Punch. Then he sent out his Steelix, which became easier and easier to take out fast thanks to my increasing attack from Power-Up Punch and Fighting-type moves being super effective against it. This allowed my Lucario to defeat his Steelix really easily and it could even take out almost half of Raikou's health before it fainted. Now it was time for my Groudon to shine with its Ground-type moveset. I dealt nice damage to the Raikou and then once Groudon's Earthquake was charged up I used it to defeat Raikou and with that defeat Giovanni for this month.
Now I got the chance to capture the Shadow Raikou. I usually throw a Silver Pinap Berry for my first throw on any Legendary Pokémon as it increases the chance to capture like a Razz Berry does and it gives extra Candy like a Pinap Berry. As you can see in the next screenshot I was able to catch it with the first throw and got the extra candy from the berry!
Now that I caught the Raikou it's time to appraise it and see if I was able to get a good one.
This one has 9 attack, 10 defense and 11 HP. Making its overall IVs a lot better than the Shadow Zapdos and Shadow Moltres I caught in the previous months. :D If I purify it those would reach at least 11 attack, 12 defense and 13 HP which is pretty nice! I do have a 96% Raikou as my highest so it wouldn't be an improvement for me to purify this one for now.
Now I can start the February quest line to encounter Giovanni, which I will use to encounter Giovanni again next month who should have Shadow Entei. Then in April he should have Shadow Suicune.
Have you defeated Giovanni this month to capture Shadow Raikou ?