From Legacy Wiki
King Behemoth run
The strange hives in this map teleport you to a connecting hive, you will see one to the right when you start the raid but ignore it for now, and move past it to the other hive/teleporter to the north. In this new area, continue to head north to the next hive/teleporter, then head left in this next area to be on the final path. From here there's no way to go off track, just carry on forward to King Behemoth.
Aberation run
First you need to find 4 power sources, they spawn over 9 predetermined squares which can be seen on the map, 2 of those squares are through the first teleporter which is where you need to go when have all 4 power sources so it's best to skip the first teleporter and explore the rest of the map first. Once you have all 4 go through the teleporter on 3,8 (if you aren't already) and head left to the radiation cannon on 7,24. Using the radiation cannon consumes the 4 power sources you have and causes eggs to spawn in every area of the map. By walking on an egg you destroy it. Once you destroy 10 the Aberation will spawn on 2,15, so usually if you break all the eggs in the radiation cannon's area you will see the Aberation while leaving. After breaking 30 egg the Aberation respawns on 17,17.
Notes
Breaking 30 eggs respawns the Aberation, if you don't kill the first before breaking 30 eggs, it will not respawn. If you break all 50 eggs you will be rewarded with this raid's trinket upon finishing, it also rewards you a 5th power source which can be used to heal (check the notes under the King Behemoth run to learn how.)
Notes -
To spawn King Behemoth you must first defeat at least 4 NPCs.
Every time you attack King Behemoth he has a chance to teleport away from you to preset squares, you can also find these on the map created.
Also seen on the map are gang HQs and power sources, if you collect a power source and take it to a HQ you can heal, however each HQ can only be used to heal once.