"循着遗臭追踪" can be translated into English as "track down by following the stench (left behind)" or more figuratively as "pursue by tracing the foul trail".
The first option directly conveys the literal meaning of following a bad smell to find something or someone, while the second option captures the figurative essence of pursuing something unpleasant or notorious by following the evidence or signs it leaves behind. Depending on the context, either translation could be appropriate.