The Everlasting is introduced as a boss in God of War: Ragnarök.
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The Everlasting Dragon can actually be found fairly early on in the game, as you explore the Dragon Beach in Svartalfheim. You’ll see it as a dragon seemingly carved in stone, as shown in the screenshot below, but you won’t be able to awaken it until you acquire the Mystical Heirloom Relic. This can be found in a hidden area on the Lake of Nine in Midgard, but you’ll need the Draupnir Spear (acquired during the Forging Destiny main quest o access it.
One of the first attacks that the dragon will likely use is a kind of meteor shower. It will shoot burning rocks at you as it raises its neck, so look out for this animation and be ready to block the attack. There is a second element to this attack which occurs when the rocks hit the ground, at which point they explode. You can avoid this explosion by dodge rolling out of the way just before it happens. It won’t inflict as much damage as the meteor shower though, so you don’t need to worry about it too much.
The dragon will perform a version of this same frost breath attack while it’s on the ground. This one can’t be blocked or parried either, and you will have less time to respond, so be ready to perform a quick dodge roll whenever you see the red ring indicator around its head.