You can gain this achievement by going for a necromancer build.
Gem skill to use:
Summon Raging Spirit + Increased Duration/Spell Echo (to be able to cast 20 of them at the same time)
Vaal Summon Skeleton (need to be lvl up a few times)
Raise Spectre/Summon Golem. But the above should be enough
Skill Tree :
Go for all the +1 zombie/skeleton nodes in the skill tree
When you have your gems and skill tree setup it will net you:
8 zombies + 20 raging spirit + at least 32 skeletons from Vaal Summon skeletons = 60 minions !
Alternative method :
When playing, you can encounter shrine in the area. Those shrines gives you buff and sometimes the buff will cast Summon Skeleton for you (The shrine will have a skull head on top). This give you some bonus minion for your army but you'll need to be very lucky to find this kind of shrine and you can't control the number of skeleton spawned by it.
You can also look for some items that give +1 minion buff but IMO it's not really worth the effort. The 3 to 5 skills should be enough to have your minion army.