Infinite Undiscovery

This one is Big Daddy's Back. You have to beat Sigmund in the Seraphic Gate to add him to your party to unlock it.

The Seraphic Gate is unlocked after you beat the final boss and is located inside the Kolton castle. In the second level (the desert) go past the first teleporter and find the second one (located where you have to gather firewood for Aya). Go through it and prepare to face Sigmund one-on-one.

Make sure you're at a decent level of at least 70 to 80 and have the best armor and weapon you can currently buy/make. He will mostly use Grin Valesti and Alfheim in the battle, as well as a max three-hit combo. A properly timed block/deflect of the combo or Alfheim (I think it can be blocked, as long as it's the first hit) will stun him, and if you have enough AP, you can use Cutting Gavotte to knock him into the air and get a few easy hits in.

Also, set your cursor memory on in the options and set your cursor on Green/Yellow Berry potions, and bring a handful of them into battle. Also, once you clear out enemies in front of the teleporter, you can always enchant some ATK+ or others to Capell.

An unorthodox and somewhat time consuming but successful strategy is to let him kill himself. Run in circles and through the middle to distance yourself the length of the room from him, then play Alucinari on your flute in his direction. Sigmund will always attack the image, which explodes and hurts him. As soon as you play the tune run the same distance away from him and play it again, and repeat until he explodes himself to death.

To unlock this achievement you have to kill Sigmund in the Seraphic Gate.
To open the Seraphic Gate, beat the final boss of the story and go to Kolton. The entrance is in the palace (the building facing Eugene).

First of all you'll want to craft the best weapon for Capell. It's the Azureal Blade crafted by Edward. To do so:
Go to the Seraphic Gate. When you enter, the game tells you that you have unlocked new item crafts. You have now access to Item Crafting level 6 after doing some quests. Come back to Kolton, find kristopher and talk to him. Choose the answers “I’ll try it.” and then pick “It’s B>A>C". Edward is now able to learn Item Crafting lvl6 and craft the Azureal Blade.

This is what you need to have to craft the blade (assuming you have downloaded the two free DLCs A Voucher and B Voucher on the xbox live marketplace):

Azrueal Blade:
2x Amarlista (10000 Fol each in all shops)
1x Gram (construct from parts below)
1x Emblazoned Sword (given to you buy Sigmund at the beginning of the game)

To craft Gram, you'll need this:
3x Atlantis Metal (20000 Fol each in all shops)
1x Quartz (7000 Fol each in all shops)
1x Aqua Blade (25000 Fol in Port Zala shop)

If you don't have the Emblazoned Sword anymore, simply craft Gram and give it to Capell.

Now that Capell has a nice weapon, check out his enchanting skills: if Capell is able to enchant 2*3% HP Regen and +500 ATK on him, you're ready to go.

Go to the Seraphic Gate, grind some levels for your characters on the first level (I recommend being around 80 for an easy fight against Sigmund, it doesn't take too long to grind). Kill the ogre at the end of the level and come all the way back to the Kolton inn. Rest & save. Verify that you have all the material needed for the two 3%HP Regen and the +500ATK enchants.
You can also use the +1000ATK and +6%HP Regen enchants if you have unlocked them.

Go through the first level of the SG and take the teleporter. You are now in the desert where Faina asked you to find her little brother. From there, go to the location where you had to find wood to light a fire for Aya: you'll find a teleporter. Put your two 3%HP Regen and your +500ATK enchant and take the teleporter.

You are now facing Sigmund and he is ready to jump at you.
You'll have only Capell for this fight and Sigmund will never stop attacking you (that's why HP Regen is important - you won't have enough time to use healing items).

I had around 14k HP with Capell (lvl 80), on hard, equipped Gram and I had no problems.

Sigmund's HP (normal/hard/infinite)
130,000 / 156,000 / 234,000

As you can see, he doesn't have a lot of HPs.
Put Grinn Valesti to the B button and prepare to spam it. It should deal around 20-30k damage so the fight will be very short.

Sigmund uses Grinn Valesti and Alfheim.
Simply attack once, run away if he touches you (so the HP regen will heal you), and when you're 100% life, attack him again. Always with Grinn Valesti.
His attacks are easy to avoid. He doesn't deal massive amount of damage on normal and hard but you have to be more careful on infinity (on this difficulty, he can deal 10k damage in one hit so do not get close to him if you have not at least 10k HP remaining).
If you wait the good moment to attack him, he should fall pretty quickly. Don't forget that he always can kill you easily if you're not careful - but you should have no problems.

Once you've killed him, he'll join your party.
He is still level 20 or so but he has a great sword that you should put on Capell instead ! ;).

PS: Please correct any mistakes I made, I'm not a native english speaker.