This achievement requires the completion of 72 Variant Adventures.
Variant Adventures are different settings of an adventure with possible changed restrictions, objectives, requirements, and rewards. Once you complete a regular adventure the variants will unlock of varying difficulty. Also, if you are participating in events they have Variant Adventures which count towards this as well.
Adventure Variants can involve reaching the same Area or higher than the original mission, taking up slots in your formation, additional enemies spawning, etc. There are many different ones to look out for.
As you progress this far in the game you should have a pretty good idea what ones you can complete. For example, if you can reach Area 200 in free play there is a good change you will be able to complete the Variant that requires reaching area 150 (depending on the modifiers).
I would recommend trying to complete all the Variants during the events as they are generally a bit easier. If you are having trouble completing a particular variant you may need to unlock more heroes ,take advantage of a weekend buff, or use some potions.
A full list of Variants can be found here:https://idle-champions.fandom.com/wiki/Adventures