On the island in the snow biome sometimes wild gigas can get stuck on the small icebergs littered across the river that creates the border between the snow and jungle biomes and the water is shallow enough for them to not drown so you might not even need to build a taming pen.
I dare you to raise one!! They are savage if you got two high lvl parents (about lvl 140ish) and you get imprinting on it. The thing will become an adult with about 230% melee and basically one chomp any bronto!!! But on the down side you loose your job and your girlfriend
Make 4 metal dino gates and 1 large bear trap. Place three frames and door into an incomplete square and the large bear trap in the I between them. Lure the Giga into the trap and while its trapped place 4th down to make the square. Then just light it up with tranqs