Flew to Twinleaf Town and walked over to Lake Verity. I Surfed to the island in the centre of the lake and headed inside the cavern. There, I saw and talked to Mesprit, but it then flew away. Prof. Rowan then showed up and talked to me for a bit, telling me that I could search for Mesprit as it travelled around the region. I didn't care about doing that yet, though, since all I wanted to do for the moment was have it recorded in my Pokedex.
After that, I returned to Lake Valor and went inside the cavern there. I saved in front of Azelf and started a battle with it. This Pokemon was quite annoying for me to catch, since I quickly found out that my Pokemon couldn't weaken it to red health without killing it. Also, Azelf's Nasty Plot + Swift/Uproar was irritating since it did so much damage. I ended up soft resetting and leaving to get my Giratina from the PC so that Azelf's Normal type moves wouldn't have any effect. I captured Azelf after several Dusk Balls.
With Azelf caught, I flew to Snowpoint City. I will head over to Lake Acuity again next.
After slaying Barry at the Pokemon League's Pokemon Center, I went back out to Victory Road and I trained my team inside the cavern for almost two hours until all of my Pokemon were above Lv. 60. I returned to the Pokemon League building afterwards and I finally entered Elite Four Aaron's chamber after taking a lift up. I challenged him and he used his Dustox and I beat it with Staraptor's Aerial Ace, which was super effective. Aaron's Drapion was slightly more problematic though, but I still beat it with Lucario. I used Infernape's Flamethrower attacks to beat Aaron's Beautifly and Vespiquen next, then my Staraptor thrashed Aaron's Heracross with Aerial Ace. Once Aaron had lost, I quickly healed my team.
I walked over to Lake Acuity and headed inside the cavern located in the middle of the lake. After saving my game, I started a battle against Uxie and lowered its HP to the red range using Starmie's Thunderbolt and Psychic moves. I started throwing Dusk Balls after that and was lucky enough to catch it fairly quickly.
Once Uxie was caught, I had finally accomplished seeing every Pokemon in the Sinnoh Dex. I returned to Sandgem Town and stopped by the lab. I talked to Prof. Rowan and showed him my Pokedex, then Prof. Oak from Kanto showed up too. Oak upgraded my dex to the National Dex and then told me that the Pal Park was now open for business. Rowan then gave me the Poke Radar item.
After healing my Lucario with Super Potions, I left Aaron's chamber and walked through a corridor towards Elite Four Bertha's room. Once there, I shifted my Pokemon around and I finally battled Bertha. First I used my Roserade against Bertha's Quagsire and that battle ended fast thanks to Roserade's Petal Dance attack. Bertha used her Sudowoodo afterwards and it lost to Petal Dance as well. I used my Floatzel against Bertha's Golem and Hippowdon next and both fainted due to Floatzel's Surf, but Hippowdon's Sand Stream ability lingered. I battled Bertha's Whiscash last and Roserade's Giga Drain defeated it swiftly. I healed my Pokemon once again and I headed through another corridor and saved after taking a lift.