Sometimes items are not obtainable during hunts. Some of the items are obtained through
specific quests or events. Some items exists in a game but does not.

For example: Epsiguard is said to exist in PSOBB but it's not obtainable in any other way.
Also, the Schtserv is working on the item "Cladding of Epsilon" for the drop
item of Epsilon. Last information is, Cladding of Epsilon does not exist in Schtserv, but
they're trying to make it real in the game in further future. Before I forget,
"Epsiguard" is a shield that is meant for androids to use.
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Here are some items that are obtainable through quests/events:

Girasole (Doublesaber)
-A prize in "Black Paper's Deal 2" on Ultimate Difficulty
-A MA4 prize for killing 15,000 monsters in each Episodes (including 2,000 more for each
Episode), you can talk to Montague for this prize

Izmaela (Slicer)
-A prize in "Black Paper's Deal 2" on Very Hard Difficulty

Libera Kit (Mag Cell, used to make Agastya Mag)
-A prize in "Black Paper's Deal 2" on Hard Difficulty, chances are low to get

Raikiri (Katana)
-It can be obtained in a Christmas Event on Ultimate Difficulty

Solferino (Wand)
-It can be obtained in a Christmas Event on Very Hard Difficulty

Siren Glass Hammer (Rod)
-A 1st Place prize in MA4 Deep Sea Rendezvous with 7 Lucky Tickets
-It can be obtained in a Christmas Event on Hard Difficulty

5th Anniversary Blade (Saber)
-It can be obtained in a Christmas Event on Hard Difficulty

Honeycomb Reflector (Shield)
-It can be obtained in a Christmas Event on Ultimate Difficulty

Kunai (Card)
-It can be obtained in a Christmas Event on Ultimate Difficulty
-Obtainable on Ragol Onslaught Event

Meteor Rouge (Launcher/Cannon)
-It can be obtained in a Christmas Event on Very Hard Difficulty

Tension Blaster (Handgun)
-It can be obtained in a Christmas Event on Ultimate Difficulty

Great Bouquet (Saber, an odd item to be a weapon)
-It can be obtained in a Christmas Event on Normal Difficulty

Daisy Chain (Sword)
-It can be obtained in a Christmas Event on Normal Difficulty

Genpei (Shield, the shield matches ID whoever wears it)
-It can be obtained in a Christmas Event on Very Hard Difficulty

Samurai Armor (Armor)
-It can be obtained in a Christmas Event on Very Hard Difficulty

Toy Hammer (Katana, very odd item to be a weapon but powerful, and yes, what the heck)
-It can be obtained from Offline Challenge Mode
-It can be obtained in a Christmas Event on Hard Difficulty

Lollipop (Cane, EXTREMELY odd item to be a weapon, but it's real funny if you try to lick
it)
-Trade 15 Photon Tickets to Paginini on the quest "Gallon's Plan"
-It can be obtained in a Christmas Event on Normal Difficulty

Stealth Suit (Frame, not very helpful armor with 1 DFP boost but also 300 EVP boost)
-Trade 20 Photon Tickets to Pagnini on the quest "Gallon's Plan"

Ken'ei Tousho (Card, a very, very old coin...)
-Trade 10 Photon Tickets to Pagnini on the quest "Gallon's Plan"

Chameleon Scythe (Partisan, I have no idea why is it called that, it does have a
chameleon)
-It can be obtained in a Christmas Event on Hard Difficulty
-It can be obtained from Offline Challenge Mode

Rambling May (Shot, adorable gun for women, yet powerful)
-It can be obtained in a Christmas Event on Very Hard Difficulty

Commander Blade (Saber)
NOTE: It says "Only Team Masters can use this weapon", but it must mean Leader
Ranks and Team Leaders can use this weapon. But it just signifies great leadership and
teamwork, and when this is equipped, all other Team Members in-game gain 20 ATP boost.
-It can be obtained in a Christmas Event on Hard Difficulty
-Team Leaders can purchase this weapon for 8,000 Team Points

Three Seals (Barrier, best shield for Forces)
-It can be obtained in a Christmas Event on Ultimate Difficulty
-It can be purchased from a wandering Tekker in the city for 10,000 Meseta on Mondays and
Saturdays

Armore Rose (Card, eh)
-It can be obtained in a Christmas Event on Ultimate Difficulty

God Shield series (Shield)
-Any one of these shields are obtainable from Offline Challenge Mode
-Any one of these shields are obtainable from Gallon's Shop from the Roulette Game

God Shield "Kouryu" (Shield)
-Trade all 4 God Shields for God Shield "Kouryu" in "Clarie's Deal"
quest

Two Kamuis (Daggers, these are extremely useful for Hunter Androids those who can't
Zalure)
NOTE: This item only exists on "Clarie's Deal" quest and you must fight the
Spirit of Shino for it. After then, you must trade the 3 Book of Katanas and the 2
separate Kamuis.

Book of Katana 1 (Unique, used for Two Kamuis, hold on to it)
-Offer all fake Agitos for Book of Katana 1 on "Clarie's Deal" quest

Book of Katana 2 (Unique, same as Book of Katana 1)
-Offer Musashi, Yamato, Asuka, Shichishito and Sange for Book of Katana 2 on
"Clarie's Deal" quest

Book of Katana 3 (Unique, this one should be really easy to get)
-Offer Kusanagi, Yata Mirror, Red Odoshimaru, Black Odoshimaru and Yasakani Magatama for
Book of Katana 3 on "Clarie's Deal" quest

Mercurius Rod (Rod, extrememly useful for Forces who would want to boost Grants like mad)
-Offer Glide Divine, Brave Hammer, Caduceus and King's Striker for Mercurius Rod on
"Clare's Deal" quest

From the Depths (Shield, the ultimate shield and can only be obtained from Clarie's Deal)
-Offer Secret Gear, Flowen's Shield, DF Shield and De Rol Le Shield for From the Depths on
"Clarie's Deal" quest

Angel Ring (Shield, also known as a "HALO")
-Offer Sacred Guard, Light Relief, Rappy's Wing and Magic Rock "Moola" for Angel
Ring on "Clarie's Deal" quest

Elenor/No PB's (Mag, rather useless but usable for Androids)
-Complete Rico's request on "A New Hope" quest and talk to her

Elenor/With PB's (Mag, VERY, VERY, and I mean, VERY expensive item, read below)
NOTE: This is obtained in Lobby 13 (any ship) in the Casino for 9,999 Daily Tickets

Principal's Gift Parasol (Partisan, for lovely ladies to use, but they pack a punch with
it)
-Obtained from "Black Paper's Deal" quest on Very Hard Rappy Route
-Purchasing a 30hit PGP from the Casino (Lobby 13) for 9,000 Daily Tickets

Shouren (Katana)
-Obtainable from "Black Paper's Deal" on Ultimate Difficulty Dorphon Route
-Obtainable from "Black Paper's Deal 2" on Hard Difficulty

Master Raven (Handgun, bastard gun for males only)
-Obtainable from "Black Paper's Deal 2" on Normal and Hard Difficulty

Last Swan (Handgun, pretty gun for females only)
-Obtainable from "Black Paper's Deal 2" on Normal, Very Hard and Ultimate
Difficulty

Union Shield (Shield, the color of the shield depends on what order in game parties and ID
of the user)
-Obtainable from "Black Paper's Deal 2" on Normal Difficulty

There are probably more Quest Items but if you find anything I'm missing, feel free to
post a comment or send me a PM. If there's any errors, please notify me on the PM's.