When taming a Giga it's torpor drops in 2min so wait til it's torpor is at about 4,000 then pump a several hundred Narcotics all at once. 100 Narc = 4,000 torpor. It takes longer for the torpor to rise than it does to drop. Took mine 30min to go from 4,000 torpor back to max.
Start by crafting 4 Metal Dinosaur Gateways and Large Bear Trap. Place 3 Metal Dinosaur Gateways in an open square formation, but don't connect them, leave small spaces in the corners. Place a large bear trap in the center, and lure the Giga into it. You'll have seven seconds to run around and place the fourth Dinosaur Gateway. Now the Giga is pinned in the square, use whatever method of applying torpor you like, but I highly recommend using your best Crossbow, arrows are cheaper and a better investment than darts.
When I find a giga, I lure it to a location I find easiest to get it stuck. Easiest way to lure it is by placing a dodo or a monkey on the platform on your quetz. It'll register as a land dino and remain aggressive to you. Then get it into a position where if it runs away it gets stuck. I do this with natural traps and solo. Good luck.
It takes a lot more tranq darts than you think... Dex said around 410 for the lvl 135 we just took down, it was more like 800 darts (with a ram rifle) and 150 arrows (with mc crossbow)... bring ALL the darts!!!
You can probably do this but im not completely sure but heres a challenge:
Get a friend and make them get a crap ton of meat you yourself get a bow and tranq arrows find a giga and unload them tranqs (make sure you have narcotics)and start taming! Not easy but a challenge (get into leather armor for a good challenge)