As you explore the spooky woods to the south of the Orphanage, you will meet a very scary tree. This chap might be a bit terrifying, but he is actually just a little lonely, and as he cannot catch Nexomon himself, he asks you to catch some for him. The tree wants a Griffgar and a Dreaver to be friends with, and if you can find them, he will reward you handsomely.
The main issue in this quest is actually finding the two Nexomon that the tree wants, and it can take a lot of searching to find the spots where they spawn. Below you will find the two areas near the tree that seem to spawn Griffgar and Dreaver with any degree of regularity.
Where to find Griffgar
The best place to look for Griffgar is back on the first screen of the woods where the NPC is trying to build up the courage to continue further in. In the row of bushes at the bottom of the screen, Griffgar is a pretty regular spawn.
Where to find Dreaver
The best place to find Dreaver is just to the south of where you meet the tree. There is a bunch of bushes there where Dreaver will spawn.
You will need to have both of them in your Team to be able to trade them with the tree, so make sure you send them to your Team and not to storage when you catch them. When you go back to the tree, he will trade you a Vault Key, a Golden Nexotrap, an Experience Core, and a Greed Core for the two Nexonomon.