I started doing my task on the part of The Spike for 80 level+. Obviously, it's possible to do the task on a low level but for me, it was quite challenging for a really low level and really long.
When you are kinda "high" level, doing all the tasks on the lowest floors is not that hard. I did all four tasks every day. However, if you don't want to run through the whole Spike looking for the necessary items/NPC, you can just stick to the killing mission, where you have to kill 7 drillworms . This, however, will take you a long time to complete the outfit.
I liked starting on the high floors, checking for the hotspots there and then making my way down. As the monsters there are not that densely spread. But if you don't want to go from one spot to another (because the hotspot you are looking for might be the last one you go to), you can skip this task entirely.
The other two tasks are pretty straightforward since the NPCs are located on maps,
Summing up, if you want to do it in the shortest time possible, do all of them. If you want to be safe and don't care how much time in total it will take you, just go for the "Kill" mission.