The Wonder Women fought several foes in common, proving how timeless their tales were across the Multiverse. Two such foes were apt for bending time to fit their agendas.
The Time Trapper was a mysterious entity, more known for his conflicts with the 30th Century Leion of Super-Heroes. When he first appeared, this entity faced Earth-One's Wonder Woman as Ty M Master, and would later reappear to bedevil Wonder Woman and her allies the Super Friends.
On Earth-Two, it was Tibro the Crime Master of Time who appeared, himself appearing as one of several individuals from different time periods while tormenting the 20th century. Although Ty M Master used a funhouse to torment the Amazing Amazon and her beau Steve Trevor, Tibro simply sent the pair to an ancient era. While Ty assumed the identity of Commissioner Wilson in the 30th Century, when facing the Legion of Super-Heroes, Tibro assumed the alter ego of Colonel Trevor himself.
Tribo's future influence was apparently ineffectual, though his twin claiming the name of Time Trapper would erect a barrier in time to hold back the Legion (in much the same was that Earth-Two's Tempus had done, when the villain Per Degaton repeatedly attempted incursions into the future of that world and was instead sent to interdimensional Limbo as had the Flashs of two Earths when they faced Tempus in the timestream).
It was later revealed that the more well known Time Trapper was a Controller and pawn of the original Time Trapper. It was later ascertained that the original was the evil future version of Legionnaire Cosmic Boy, who's counterpart Black Condor left his native Earth-Two for Earth-X and was replaced by an evil Nazi soldier from that other world. So that Nazi and the evil deviation of Cosmic Boy were themselves dopplegangers, in a sense.