Pardon any inaccuracies, it's been a long time since I played but this game doesn't change much so my advice is still accurate on a technical level.
Those enemies have a "damage threshold" mechanic, in the sense that if you hit them with something that doesn't have a high enough "calibur", it will fail to deal damage that will count for a knockout.
The most accessible way to deal damage that counts for a kill is to use the shotgun. As a bonus it will knock giants down, however on low upgrade levels for reload speed, you will only just barely reload in time to be ready to make another shot to stun him, so prioritize upgrading your shotgun reload speed to a functional degree ASAP.
Grenades and RPGs are also functionally capable of dealing killing blows against giants.
I do not remember if rifles were able to count for lethal damage.
My verdict: shotgun shells are valuable. They are your cheapest option for killing these enemies that would otherwise be unstoppable. RPGs are vastly too cumbersome in ammunition and speed to justify, unless you're using Cheat Engine for infinite ammo then have fun exploding the world. You can get by with grenades if you managed to hurt the giant with shotgun shells prior and you ran out of ammo or think reloading is too costly for your time.
However yes, the giants are brutal and the egg-throwing minigame is absolute hell to play and win fairly, because you use gold eggs to stun and kill the giants yet they are also your healing in that mode. I think white eggs are the lowest threshold that can kill giants in that mode but they deal abysmally low damage and have no benefit to stun. So functionally, don't count white eggs and use only gold. That mode will eventually send giants in squads of 3 while you have to headshot them with golden eggs that are thrown slowly and managed with clunky keybinds that might make you accidentally eat the egg you're throwing. Walk in there at your highest level of preparation, with or without Cheat Engine.
