Infinite Undiscovery

Forge many Genius Quills and Halgition papers and write Memoirs of a Mercenary 60 times.

Use 30 on capell.
Use 10 on ed.
Use 10 on touma
Use 20 on Michelle.

This should give capell well over 1 million hp and significantly increase the HP of your other characters.

Its time consuming, but do it this way and the fight is long, but VERY EASY.

Just to provide more information than the other solution, this achievement is for beating the last boss of the Seraphic Gate (the post-game dungeon unlocked when you complete the game) on HARD difficulty.

Starting from the beginning, you will need to beat the story on normal to unlock hard, then beat the story on hard. Load your clear save on hard and you will be able to enter the Seraphic Gate from a portal in the castle in Kolton.

Signum7 has an excellent guide for tackling the Seraphic Gate which can be found here: http://www.gamefaqs.com/xbox360/935661-infinite-undiscovery/...

For the boss fight itself, it is covered in Signum7's guide but I can provide some extra info from my experience. As you should know, the Queen is the hardest boss in the game. When I went for my first attempt i was able to mop the floor with all other bosses but got my butt kicked by her.

When I did defeat her, My party consisted of Capell, Edward, Komachi, and Eugene, all with the best gear I could craft and all around level 170. You can use whatever party you feel comfortable with, just know that the tankier characters that use heavy armor will be safer. Obviously, the higher level you are, the easier it will be.

To make the fight easier you can use the Memoirs of a Mercenary strategy from the other solution to boost everyone's health. At my level I only used enough to boost everyone past 99,999hp and the fight was easy enough, so don't think you need to farm so much to get to millions of hp. An important part of this strategy is to have everyone equipped with an hp% regen item so that they will maintain themselves easily.

To do the crafting you will need to level up their ICs and do the IC upgrade quest
Memoirs of a Mercenary: Rico w/ Genius Quills and Halgitan Paper
Genius Quills: Seraphina w/ Dragon Fangs and Pius Wood (both farmed from baddies in Gate)
Halgitan Paper: Michelle w/ Kenaf Cloth and Lentesco Wood (bought from Halgita general store after the shop upgrade quest)

NOTE: If you are going for the Seraphic Gatekeeper achievement for beating the Queen on infinity difficulty, you will still have to beat her on hard as beating her on infinity will not unlock both achievements.