Before doing anything, what you'll want to do is rest at the Wandering Traveler, the little outdoor inn that usually shows up around Halure and Aspio, before the story events at Dahngrest. You want to do this in order to kick off the side quest chain involving Rich, and you risk missing your chance if you defeat the first monster at Keiv Moc before learning about this quest.
One last thing to note before getting into the list proper is that Giganto Monsters each have unique material drops, often used to make powerful end-game equipment like Yuri's Garm Fang. These drops aren't guaranteed, so you can save yourself some headaches in the long run if you reload until you make sure to get the item from each -- equipping a Hunter's Monocle should help. The monsters will eventually respawn, and you can get the items from their memory versions in one of the Post Game dungeons, but it's usually easier to just make sure to get the items early on.
Green Menace - Forest of Keiv Moc
This monster is pretty much right on the main path in Keiv Moc, after the first set of events at Dahngrest. He'll probably be pretty tough to take on when you first see him, but not impossible. Just make sure to have already talked to Rich before defeating him. He drops a Green Menace Claw.
Hermit Drill - The Weasand of Cados
This one is also pretty hard to miss, and you'll probably find him not to difficult to take on your first time through the Weasand of Cados. His drop is the Great Crab Shell.
Medusa Butterfly - Sands of Kogorh
This Giganto is on the west side of the second region inside of the Sands of Korgorh. He's not too hard to miss, but the area is pretty sprawling and you have the water-level mechanic your first time through on top of that. They drops Dragon Powder, which you will need a couple of to make some gear for Rita.
Chimera Butterfly - Quoi Woods
You'll need the Sorceror's Ring Level 4 for this guy, which you can get by visiting the aer krene near Nordopolica late in the game (you may also be able to get it from another one of the krenes.). Once you're able to burn obstructions with the ring, return to Quoi Woods and enter from the east side. You'll encounter the Chimera Butterfly here as well as one of the Fell Arms. The boss also drops Dragon Powder.
Brutal - Peyoccia Plains (South of Halure)
Likely the first Giganto Monster you'll encounter the resides on the World Map. South of Halure right before you enter Deidon Hold, you should be able to fight this guy late in the game. He's usually pretty easy to encounter when going to revisit Zaphias after Estelle leaves the party during that section of the story. He drops the Long Horn.
Pterobronc - Mt. Temza
This guy is literally right in front of you early in Mt. Temza. He drops the Great Raptor Beak. You can get another beak near the top of the mountain once your Sorceror's Ring is level 3 or higher.
Brucis - Egothor Forest
You can fight this guy pretty early relative to a couple of the others, before you even get to Myorzo. During the story events at Egothor Forest, keep following the path to the east and this boss resides in the southeast corner of the area. Like most of the Gigantos, he can be pretty tough if you attempt to take him on your first time through, though. HIs drop is the Bull Wing.
Griffin - Northeast Yurzorea (East of the hot springs)
East of the hot springs, just before the mountains, you have a good chance of encountering the Griffin, who drops the Griffin Claw.
Poseidon - The Enduring Shrine of Zaude
Another dungeon Giganto that is impossible to miss, and his drop is just a Rare Metal.
Fenrir - The Erealumen Crystallands
Early in the game's final act, you'll enter The Erealumen Crystallands during your quest to gather the four spirits. Near the end of the dungeon, you can find Fenrir waiting in an optional area off to the east. He drops the elusive Great Wolf Fang.
Bloody Beak - Southeast Weccea
The last of the three Gigantos to be found on the world map, and a new one from the PlayStation 3 version. He can be found on Weccea's southeast island late in the game. He drops a Bloody Beak Scale.
copied from: https://www.rpgsite.net/feature/8169-tales-of-vesperia-gigan...