This is only possible post-game and requires a strong team and some preparation.
After you've finished the main story you'll be at the hospital. Check the PC for a new case from the DigiLab about a mysterious dark energy from a new location.
Bring your 11 best Mega or Ultra Vaccine-type Digimon, preferrably ones with a Light attribute and/or a DEF-penetrating attack like Ouryumon, Omnimon, etc, as well as lots of HP, SP, and revival items.
Upon your first visit you'll meet VenomMyotismon who unfortunately is NOT our vampire target and even more unfortunately is not going to let us pass without a fight. Despite this guy being taken down by two 12 year olds in the anime with one DIgimon each you're gonna have a much harder time as this fight is one of those wonderful "beat-him-as-fast-as-you-can" kind of battles.
VenomMyotismon will go first and use Number of the Beast, which will boost ALL of his stats followed immediately by Six Actions Six Boosts. This ability will automatically make VM use another ability, Raise the Roof, every six turns. If that wasn't bad enough Raise also boosts his stats even more and heals him for 666 HP. He still attacks with basic moves like Venom Infusion and Nightmare III but he'll repeat the cycle of boosting his stats every six turns until he can one-shot your Digimon and all you can do is watch them die one at a time.
My leading lineup was Susanomon, Ouryumon and Gallantmon CM (all level 99, 100% CAM, and 200 ABI) and I was able to take VM down by following a simple process:
on Susanomon's turn use Attack Charge on Ouryumon
on Gallantmon's turn attack with Quo Vadis (insta-kill isn't possible) OR heal/recover injured/fallen allies
on Ouryumon's turn attack with Eiseiryoujin
I needed to use several HP Capsule A to keep them alive and one Revival Spray to bring back Susano and Gallant when VM was on the cusp of death. It took me a while to get it right and take him down but as long as you're not attacking when you have a downed or critically injured ally you should be okay.
Now that we've cleared the entrance we get sent back to the Lab and we can turn the case in for some rewards HOWEVER there's more to do in the server.
If you go back you can then explore the remaining floors and here's where it gets tougher.
There are 30 floors in the server and 1F (the entrance) 11F, and 21F are the only floors you can save and exit on. That's right, it's a marathon dungeon and no, the Free Gate skill, Home Gates and Exports don't work outside of those 3 floors.
I won't go into too much detail about the dungeon itself, it's pretty straightforward, but if you leave the dungeon on any of the 3 floors with an access point YOU MUST START BACK FROM 1F so unless you're trying to grind levels use your High Security skill to prevent rendom encounters and conserve your items for the bosses on 10F, 20F, and 30F.
Speaking of 30F this is where the trophy-related boss is hiding. Naturally he's a brute but for some reason he's still easier than VM was at the entrance...
Prep your team with one Panic Barrier DX each (or two regular Panic Barriers for the same effect) before going into this as there's an 80% chance you'll really need them. Just like with VM we're gonna be using Vaccine and Light Digimon with DEF-penetrating moves so whatever team you beat VM with should be suitable here.
He starts with Immortal King, which provides the Safety Guard status on him. With that boost a killing blow won't affect him ONCE. He backs this up with Regeneration, which he pops automatically after Safety Guard goes and he restores 3000 HP.
His Eye of the Gorgon lowers your DEF and slaps the Panic stat on one party member (hopefully you equipped some barriers like I said!).
Crystal Revolution is a water move that hits the entire party AND restore his HP equal to what you took. If your team lost 3000HP collectively that full 3000 goes right back to him. He also uses the basic attacks of Ice Archery, Nightmare, and Hell Crusher (all tier III) and a Mental Break Field for good measure.
After you win there's a cutscene, some dialogue, and your trophy will pop.
You can return to the dungeon for the other items like medals and memories if you want or you can just use this place a training ground for your Digimon.
Also you can speedrun the whole 30 floors (Acceleration skill + High Security skill) and keep defeating the Vampire King endlessly. As you do it counts as a credit for the Someone Special and Partner to You Only trophies so if you keep doing the dungeons with the same person/Digimon you can knock them out too assuming you haven't already.