Four catalog lines name a method that is not a normal shop buy.
HellFire and Plasma
HellFire is Fire evolved. Plasma is Lightning evolved. The badges do not list kill counts or playtime. Extra requirements on showcase pages are not copied here until they match a catalog line.
WitchCraft
The badge gives two ways. Learn to cook potions from the witch, or get hit by a secret potion thrown by someone who already has WitchCraft.
Necromancy
The badge says the element lets you summon skeletons around the arena. It does not say how the unlock starts. A badge video includes a Necromancy chapter, which confirms players hunt it as a badge element.
Elements whose badge does not explain the hunt
Celestial, KillStreak, Nova, Sand, Ghost, and Dragon have unlock badges with no steps in the description. Dragon is also a 1,199 Robux gamepass with flight, fireballs, map throws, and a dragon-boss form. The pass is a purchase path. The badge does not say it is the only path.
Shop elements such as Fire, Water, Earth, and the rest of the community index are separate. They are not these badges. Their Diamond prices are whatever the lobby shows.