To unlock the Time Traveler achievement, all you need to do is obtain The Neuroplasticity Calibrator from Otar Botkoveli before you talk to Koller for the first time, i.e. before you even start Mission 3.

1. When Mission 3 starts and Koller calls you, don't try to reach his place. Instead, travel to the Plaisade Bank station in the subway.
   
2. From the station, exit and turn right while facing the Tubehouse electronics shop and then turn left a few steps down the street to see a wooden door.
   
3. Jump over the door and enter the sewers via a manhole on the ground, then turn turn right while facing the ladder to find a locked door.
   
4. Go near the door, wait for the cutscene where a mobster tells you to get lost, and jump on the pipes above the door.
   
5. Then simply sneak into the place and find the safe on the second floor of the secret place. The code for it 4863, but you can hack it easily as its security is only Level 1.
   
6. Grab the Calibrator and sneak back out from the secret place, then move on with Mission's 3 objective.
   
7. At the end of the Augments tutorial, Koller will mention the calibrator and you will be able to choose whether to refuse the side mission or give him the item. You know what to do.

That's it. When the cutscene ends, the achievement will unlock.