Having done the Withered Army game on five characters, I think of it as having the following stages (often taking 2-3 runs per stage):
1. Get the +25% health and anti-fear upgrades, and perhaps the first mana rager (probably on a second run). No bosses are required, so the major threat is the arcane elementals. You don't have enough DPS to burn them down quickly, so figure out how you're going to interrupt at least one cast and stop their explosion. Also pull them carefully so that you can use berserking withered on them without pulling additional mobs. Sometimes I pick up the bank item if I have a spare five withered at the end of a run, because it's so useful. I usually don't pick up the first berserker yet as I don't feel comfortable going up against the boss it's behind.
2. Get past Dro. I usually get up to the 2000 mana cap and bring in 20 withered for this, and just beat him up with sheer numbers. Do figure out if you can stop him from charging around and killing your army; any kind of root, stun, polymorph, or knockback will work. If you're not a tank, he may kill you, so pick up the Thalryssa buff (this is irritating because you'll have to farm another 50 ancient mana after getting the buff, but whatever) so that Dro dies on the shield instead. With Dro dead, you have access to the starcaller, spellseer, and second berserker, and (behind a boss) the second mana rager. You probably also have a big enough army to easily pick up the first berserker.
3. Get past the Elfbreaker. With around six of the aforementioned upgrades you should be able to burn down most enemies if you start with 12-15 withered. Let the ettin grab and kill one withered at a time as he does so very slowly, and use stuns/etc to interrupt his stomps. With the ettin dead, pick up the +25% damage upgrade. If you still have a big army left afterwards, you can kill the end boss, but you might want to instead go back and pick up other upgrades you haven't gotten yet, as the only reward behind the end boss is a pet. (On the other hand, you can pick up a fair number of withered on the run up to the end boss.)
4. Get the box of calming whispers. This is a huge upgrade but requires killing 3+ arcane elementals at once, and having two berserkers in your army to open the door. I usually go big and build up an army of like 35 withered (starting with 20) before going in, but you probably don't need to.
After all that you can start with just eight withered and trash the place, picking up enough withered along the way to sweep up any remaining rewards (pet, toy, AP item, bank item if you didn't already get it).