You can reach the Centra Ruins - and hence hunt for the Odin GF - anytime after the events at Fisherman's Horizon, after you have control of a mobile Balamb Garden. The Centra continent is a shattered collection of landmasses on the south-central part of the world map. Specifically, the northern collection of these landmasses look as if they were sundered by some impact, and fittingly enough it's known as the "Centra Crater" on your map. You'll find the Centra Ruins on the western part of this Centra Crater landmass.
Before attempting this quest, you probably want to learn Diablos's Enc-None ability and make sure you have it equipped. This run is timed, and having to kill trash mobs every five steps is not conducive to your ultimate success. Also consider boosting your Magic stat boosted somewhat so you can draw spells more easily and keep your HP low so you can spam limits. There's method in this madness, which you'll see shortly.
Note: Don't worry too much about the timer for this phase, if it runs out you'll just be expelled from the dungeon and can pick the "Try Again" option. You'll keep whatever progress you had as far as solving puzzles and interacting with objects, so you lose nothing of significant value this way... you know, except for precious moments of your life. Ah well.
Once that's done, enter the Centra Ruins and head up to reach the ruins proper, the screen where you may have farmed Tonberrys earlier. This time head through the arch and up stairs. In the next screen, if you head right and up around a fountain you can find a Drain draw point, for what that's worth. Go left and up to reach another flight of stairs and follow it up. On the next screen, enter the building, go some some stone steps and stand on a stone cube which turns out to be... an elevator? Weird.
When the cube deposits you on an upper screen you'll see two ladders. If you go up the right ladder you can find an Aero draw point, which is fine... but it's not why you're here. Climb the left ladder instead and when you reach a small landing, climb another ladder and enter a tower to find some... device. Whatever, glowing light, interact with it, some machinery will spring to life and no discernible advantage will have been gained. Hmm...
Climb down the ladders to reach the ground again and interact with another device between the two ladders to create a staircase to the right. Follow it up and past a familiar screen, exiting to the right again over the Aero draw point to reach a new, higher screen.
Ascend a dim ladder near the stairs, on the left-hand side of the screen, then interact with a gargoyle statue and pluck out its eye. Climb back down the ladder, take the stairs up to the right to reach the roof. Abandon the stairs and if you go right you'll find a Pain draw point, which is an excellent spell if you don't already have it. Otherwise go left and climb a ladder to find a second gargoyle statue, this one possessing the eye the other was missing.
Insert the eye you stole from the previous gargoyle to get a code (make a note of it - like the student ID found during the Tomb of the Forgotten King, it's random) then take both eye from this gargoyle and climb back down and make your way to the first gargoyle. Insert both eyes into this gargoyle as well and a brazier will light up, showing off a row of numbers. Use the directional buttons or analog stick to enter the code given to you by the first statue, with the right-most number being entered at the top, and the left-most number going on the bottom.
Note: Unlike most progress in this dungeon, the random numbers the upper gargoyle gives you is reset each time you exit (or are expelled). This means you'll have to possibly collect both eyes again, insert them into the upper gargoyle, get a new code, then enter it if you leave, a process which can take around 3:00 off the Odin clock. Not a deal breaker, just something to be wary of. If you open the door first, however, it'll remain open on subsequent visits, so it's the progress goal you should strive for.
With this done, a door should open below you. If you're hurting for time, exit the ruins and return (or just wait for the timer to run out), as Odin awaits you beyond the open door... And unlike the rest of this endeavor, if you run out of time while fighting Odin, it will result in a game over. You'll want as much time as possible for this fight.
Boss - Odin
Odin is an odd bird. He doesn't attack, your only limitation in this fight is the timer. If it runs out, he'll finish you off with his Zantetsuken attack, which will result in a game over and loss of progress... well, it's supposed to anyways, but the PC version is somewhat buggy and the fight might not end when the counter runs out, making it impossible to lose.
|Status Resistances:||Immune to most status effects; The End 0%|
|Draw:||Death, Double, Stop, Triple|
|Drop:||G-Mega Potion x8|
All that said, Odin isn't a terribly challenging opponent, boasting a measly 4,000 HP at level ten, rising only moderately to 10,000 HP at level thirty, and capping out at 31,000 HP at level one hundred. For any reasonably-leveled party, a Tonberry should have had more HP, and the Tonberry King certainly did. He is immune to gravity, however, so if that was your crutch earlier... well, you just shouldn't need it against a foe with such trivial HP. If you entered with low HP yourself, you can just spam limit breaks to win the fight in short order. It's not like Odin's going to attack, right?
If you've got plenty of time, consider collecting some choice magic and items from Odin, as he has the Triple spell - an excellent spell for junctioning to numerous stats. Triple is the 4th best Str-J (likely the best spell you can get full stocks of now for this), 2nd best Mag-J (easily the best spell you'll get for this purpose until you have full Ultima stocks), the best Spd-J, 2nd best Eva-J, best Hit-J and 3rd best Luck-J. For general purposes, Magic is your best bet, and you'll noticeably better off if you can walk out of this fight with three full stocks, which requires a decent Magic score in its own right. You can also Mug a Luck-J Scroll from Odin, in case you want to start boosting a character's Luck stat. A somewhat dubious endeavor, perhaps, but it's still more interesting than the eight G-Mega Potion items you'd otherwise get as a drop.
Defeat Odin and you'll get your customary 20 AP, the Odin Card and his services as a GF. Or rather, a pseudo-GF, as Odin doesn't function quite like other GFs. He can't be junctioned and you can't summon him at will. Instead, he'll randomly appear at the start of fights and cuts down your enemies for you. Kind of annoying if you're trying to keep your level low, Mug specific items, draw spells, or anything more sophisticated than outright killing the foe, but if that doesn't bother you, then Odin is an interesting enough addition to your arsenal, albeit one you won't have any control over.
Note: While Odin himself is... a mild nuisance, if you're trying to avoid gaining XP, he'll later be replaced by another GF, which can interfere with Angelo Search. If you don't want either of these random events occuring for various reasons, your only option is to refrain from obtaining Odin. If you wait until later in the game, it'll be possible to return to capture Odin without him being replaced later, if you wish.