Get a snow owl or argy and make sure it has a decent amount of life. Find your Giga and get slightly out of range of it. Set up 4 metal behemoth gates in box formation, but leave the door off the 4th wall facing the Giga. Get on your snow owl and aggro him. You may need to be low for him to follow, so do expect 3-5 bites from it as you lead the Giga into the cage, but often you can do it damage free. Each bite ranges from 200-500 damage depending on lvl, so make sure you can survive the damage.

When you fly up against the back wall, let him bite once more so you know he’s in. Fly up, turn around quick and hotbar the last door in, but stay above him. Fly out and land on top of the gate post. Carefully dismount... I’ve had some funny falls into the cage, but now I use a tek suit and keep my bird far away. Unless the ground is raised/rocky below, he shouldn’t be able to chomp you either way. You may need to bring a few hundred tranqs for high lvl ones, but plug away at him as he runs corner to corner. Bring some spare crossbows or rifles. Have some kibble, or mutton handy (# depending on your server rates) and throw it in his inventory when he goes down. Gigaty gigaty goo!