(covers information from several alternate timelines)
Karyn Archer was the great-granddaughter of Starfleet officer Jonathan Archer, and first officer of Enterprise NX-01 in an alternate timeline in which Enterprise was thrown back in time from the year 2154 to 2037.
Karyn's great-grandmother was Esilia, an Ikaaran whom Captain Archer rescued from a field of spatial anomalies in the Delphic Expanse. In addition to Human and Ikaaran ancestry, Doctor Phlox's analysis revealed the presence of chromosomes in Karyn's genetic structure which originated from two unknown species. Karyn served as Enterprise's first officer, under the command of Lorian, the son of T'Pol and Commander Charles Tucker.
In 2154, Lorian and his crew intercepted their counterparts, who were about to enter the subspace corridor which had transported them back in time in the first place. Lorian provided the crew with specifications with which to modify Enterprise's injector assembly, which he claimed would allow them to travel at a higher warp factor, allowing them to bypass the corridor altogether and reach a rendezvous with the Xindi-Primate Degra on time. Although Archer and his crew initially agreed to perform the modifications, he learned from T'Pol's counterpart on the alternate Enterprise that the modifications which Lorian had proposed posed a serious risk of overload, an eventuality which could have led to the destruction of the ship. T'Pol proposed an alternate plan, whereby Enterprise's impulse manifolds could be modified in such a way as to prevent the subspace corridor from destabilizing, allowing them to pass through without being thrown back in time. Feeling that Captain Archer's plan would not work, Lorian instituted a plan to steal their counterparts' modified injectors and install them on their own ship, so they could make the rendezvous with Degra. Karyn initially railed against this plan, claiming that it was too risky and that to do so would be a betrayal of Jonathan Archer. Ultimately, she reluctantly complied, even participating in a battle between the two Enterprises. When it became clear that Archer had gained the upper hand, Karyn was successful in convincing Lorian to halt the attack.
Eventually, Archer and Lorian were able to develop a plan to combat the Kovaalans, an aggressive species which patrolled the nebula in which the corridor was located. During the battle, Archer's Enterprise suffered serious damage, necessitating Lorian and his crew staying behind to fight the Kovaalans as their counterparts entered the corridor. Archer and his crew waited for five hours for the other Enterprise to emerge from the corridor, before it became clear that they would not be arriving. The fate of Karyn and the other Enterprise remained unknown. Although it seemed likely that they were destroyed by the Kovaalans, Archer also entertained the idea that their existence was negated due to the fact that the initial accident which transported Enterprise back in time in the first place had been averted. (ENT: "E²")