[Gideon Zhi]

にんぎょのまもり - Doll Charm
せんしゅぞう - Figurehead
ジグルト - "Jigult" (pretty sure this is wrong); it's a psychic ability, flanked by Longinus and Elixir.

Credits:

[Zynk]

ジグルト could it be Sigurd?

1. Music = Kosaka Asako

[Gideon Zhi]

1. Music = Kosaka Asako

Akiko, apparently, not Asako. Yay google? Character design is apparently "Kohji" as well.

[Zynk]

Apparently I just discovered how to name search with jisho 

http://jisho.org/search/%E6%98%8E%E5%AD%90%20%23names

明子 turns up a lot of derivatives "Akako", "Sayako", pick your poison 
-----------------------------
ORIGINAL WORK
I can tell that the second credits says "Yasuda"...

Again, apparantly picking radical yields a kanji for him
http://jisho.org/search/%E5%9D%87%20%23names#radical


Could be "Kin" or "Tamotsu"

安田 均; Yasuda Kin (Tamotsu, Hiroshi)

CHARACTER DESIGN
SURNAME, http://jisho.org/search/%E5%BC%98%20%23names
"Hiro", "Kouji", "Hiroshi"... there's a lot!

GIVEN, http://jisho.org/search/%E5%8F%B8%20%23names
"Tsutomu", "Mamoru" or "Tsukasa"

弘 司; Hiro Tsutomu (Mamoru, Tsukasa)

[Ryusui]

JP Wikipedia has entries for all three names:

https://ja.wikipedia.org/wiki/%E5%B0%8F%E5%9D%82%E6%98%8E%E5%AD%90
https://ja.wikipedia.org/wiki/%E5%AE%89%E7%94%B0%E5%9D%87
https://ja.wikipedia.org/wiki/%E5%BC%98%E5%8F%B8

Akiko Kosaka, Hitoshi Yasuda, and Kouji (that's the full name given).

As for ジグルト, the only thing I can find is "Sigrud," not to be confused with "Sigurd," which JP Wiki says is シグルズ (yes, "Shiguruzu"; that's not a typo).

[Pokeytax]

If the definition of Psychic is sufficiently broad and you have no other context, I would go with "Jig Lute" or "Dance Lute". But that's almost certainly wrong (Lute would be リュート).

[Ryusui]

Might I ask, what do Longinus and Elixir do? Do the names describe what they actually do?

If so, then I suggest working back from whatever Jiguruto does.

[Gideon Zhi]

Longinus does HP damage to a single target. Elixir revives. ジグルト's description is ぶつりこうげきをふせぐ which I have translated here as protecting versus physical attacks.

[Ryusui]

I may have spoken too soon on the "Sigurd" front. Apparently there is a novel by a Friedrich de la Motte Fouque, "Sigurd der Schlangentödter" (a title which translates beautifully as "Sigurd the Serpent-Slayer"), whose name is written in Japanese as 大蛇殺しのジグルト.

All told, the idea of a legendary hero's name being applied to a defensive buff doesn't seem too bizarre to me...

[Seihen]

A mis-spelling of ジグラット, ziggurat?
That's all that came mind to me.

[Hiei-]

I would also say Sigurd for ジグルト

Found a "Sigurd Hofmann" written as "ジグルト・ホーフマン"

The ド/ト ending might depend of the language it transcribed from (like "Elisabeth" which is written "エリザベス" from english but if you transcribe it from french, it should be written "エリザベート" instead to match the french pronunciation).

[Corvo]

Looking at the item description, it's most likely Sigurd.

Sigurd, also known as Siegfried, has a role in "Nibelungenlied", a german poem. In this poem, he bathes in a dragon's blood, and his skin becomes impervious to all attacks, except for a single point where a leaf adhered to his skin. According to TVTropes, there's a character named Siegfried in the anime Saint Seiya, that uses the same backstory.

[enigmaopoeia]

According to the Japanese strategy guide, they spelled it as ジグルド. Also if you're curious, it states that it does 対象の回避+25%.

Also にんぎょのまもり should be Mermaid's Amulet. The strategy guide calls it 人魚のアミュレット (Mermaid's Amulet), meaning it's 人魚の守り (にんぎょのまもり, Mermaid's Amulet) in game.

Here are some interesting changes from the strategy guide to the game, I added in my own translations to showcase differences:
バスタードソード (Bastard Sword) = バスターソード (Buster Sword).
プレートアーマー (Plate Armor) = プレイトアーマー (Plate Armor). This is spelled differently.
サイ・マンデンサ (Psy Mandenser) = サイ・コンデンサ (Psy Condenser).
アストラルアンプ (Astral Amp) = アストラル・アンプ (Astral Amp). They added a space.
ホーリーメイル (Holy Mail) = ホーリーオイル (Holy Oil).
あるびたチーズ (Arubita Cheese) = 古びたチーズ (Aged Cheese).
にんぎょのまもり (Mermaid's Amulet) = 人魚のアミュレット (Mermaid's Amulet).
ぼうぎょのうでわ (Defense Bracelet) = 防御の指輪 (Defense Ring).
ゆすらぎルーン (Peace Rune) = 安らぎのルーン (Peace Rune). They added a の.
けんじゅのいし (Cynic's Stone) = 賢者の石 (Philosopher's Stone).
やどりぎロッド (Mistletoe Rod) = 宿り木のロッド (Mistletoe Rod). They added a の.
ふるびたロッド (Aged Rod) = 古びたドクロ (Aged Skull).

If I got anything wrong, please let me know.
(Note: Thanks Zynk Oxhyde and Midna for the corrections.)

[Zynk]

サイ・コンデンサ (Thyristor Capacitor).

I think its Psy(cho)-condenser? Thyristor" sounds very complicated.. what is it exactly?

[enigmaopoeia]

I think its Psy(cho)-condenser? Thyristor" sounds very complicated.. what is it exactly?

Ah, you are right about that one seeing the ghost hunting background of the game. It's a part for a Spirit Machine used by a Scientist. I had machine parts in my head when I quickly translated it and thought it might be closest to サイリスタ開閉コンデンサ than サイコ・コンデンサ.

[Midna]

"賢者の石" translates to philosopher's stone, actually.

[enigmaopoeia]

Thank you for the correction, fixed it.