The actual description for the achievement is as follows:
As Anhur kill three enemies with a single Desert Fury
Anhur's ultimate ability (
or 4) is Desert Fury; an ability that enables him to throw his spear in rapid succession in a straight line. The spears do not do a tremendous amount of damage, but when paired up with some weak targets, or targets trapped in some sort of other ability (Ares ultimate, Xing ultimate, ect.) he can easily punish softer targets.
The key to netting this achievement legitimately is to do just that; wait for a good opportunity set-up from your team, utilize the fury relic for some extra damage, and then start that ultimate.