This is very dependent of your level, skills and intention. Do you want to start the quest from scratch and kill the final boss? Gather a team. You won't be able to solo the final boss easily, maybe at all. You have finished the access and simply want to get Crystal Splinters to farm one or two daily Caskets? Now this is possible!
First, I must assume you can collect the necessary Protective Layer and can either run or kill your way to the tasks. Warzone 7 and 8 are quite easy to run since the monster density is low and the way is short. Warzone 9 is quite challenging even for high levels. My best advice is to wear the best protection in each place. That is, mostly earth but also energy and death for Warzone 7, fire and death for Warzone 8, ice and holy for Warzone 9.
Now the tasks that are worth/possible to do solo:
Warzone 7: I wouldn't bother with those two. They are worth 10 Splinters each and are very time limited. The digging task is highly dependent on how lucky you are and the killing task time is just too low to solo.
Warzone 8: these are the two easiest tasks to solo! The scout task is fairly easy for mages because you can UH the gnome, while EKs and RPs have to be very aware of the surroundings. Destroy fire fields, wait lava holes to become inactive, shelter the Gnome from the mobs. The wax task is easy if you are fast enough in the floor tile. These will give you 20 and 10 Splinters, respectively.
Warzone 9: these are the hardest but also the most rewarding tasks. I wouldn't bother with the Mega Magmaoid task, since it's quite difficult to keep the creatures from healing each other and you won't have enough firepower to kill them in time. The fishing and the lost structure tasks are definitely possible to do solo if you know all the mechanics in there. These will give you 25 and 30 Splinters, respectively.
If you do the four tasks (2 in wz 8 and another 2 in wz9), you will get 85 Splinters, which is enough to buy one daily Casket and be left with another 10 Splinter for the next day.
Source: my own knowledge. I've been doing theses tasks in teams daily with a 900 ED and a 350 ED and solo with my 900 ED.