Gems of War

As of posting this guide there are 816 unique troops available in the game. Typically there are 3-5 added each week. You need 500 different troops for this achievement to unlock. You can obtain troops in many ways:

Chests - Gold are the cheapest, but only return Common/Uncommon base rarity troops. Guild, Glory, Gem and VIP chest all return various rarities.
Completing Kingdom quests rewards troops, including specific ones when finished.
Opening Chaos Portals in the Underworld (Delves)
"Buying" the latest troops for weekly eventns, using gems in the shop tab of said event can help getting a specific troop, but is ineffective at growing your total number.
Through the Soulforge, summoning stones produce 1-3 of 4 specific troops and these rotate weekly.

Only about 40 of the 800+ are mythic troops, which are incredibly hard to get randomly and are more effectively crafted through the soulforge.

Most long-time players will unlock this right away because they already have 700-800 troops. If it doesn't pop right away, just spend one or more gold keys. It will pop.

If you haven't reached 500 yet, there are multiple ways to earn troops or create your own:

FREE
Chests: spend keys (Gold, Glory, Gem, Event, Guild) to get Troops and other loot
Event Shops: spend Gems on Tiers and frequently get troops
Soulforge: spend Souls, Diamonds and Celestial stones to create a Legendary or Mythic troop OR spend colored jewels and Souls to create Summoning Stones which give you troops
Delve Portals: spend Chaos Shards for troops and hoard treasures
Gnomes: defeat the various Gnomes to possibly get those gnomes as troops of your own
Daily Deal: spend diamonds for set daily troops
Kingdom Quests: players who haven't gone through the story lines of certain Kingdoms can unlock an Epic level troop specific to that kingdom

$$$$ Real Money $$$$
Shop Weekly Event
VIP keys

* Don't forget to Disenchant extra Mythic level troops for a Souls reward