101Leafy researched the games.
Odyssey

Bestowed upon those who set out on a perilous adventure. Simple design, but strong.
| Class | Sword |
|---|---|
| Rarity | 6 |
| Attack | 266 |
| Slots | 0 |
| Price | 25,000z |
Upgrades
| Upgraded from | Velocidrome Bite+ |
|---|---|
| Upgrades into | Odyssey+, Serpent Bite, Hurricane, Prototype Saw-Slicer |
Can also be made new at the smithy.
Upgrade tree from モンスターハンターポータブル 2nd G 公式ガイドブック (Enterbrain, 2008), page 698.
Materials
Carbalite Ore ×4, Iron Ore ×40, Disk Stone ×40
Plus Class Tcket ×1, Carbalite Ore ×1