In order to get this achievement, you need to have a moderate to good amount of Influence with T3-M4 (easily obtainable if you choose concerned/polite conversation options with him), and a decent amount of skill points invested in Computer Use* and Repair*. This 'questline' can be initiated the moment you first meet him in the
*[
There are conflicting reports about the exact amounts required but a minimum of 15 is needed in both skills, though the actual number is probably closer to 20 - 25 for both. I'll edit this if I either discover the exact amount or someone puts it in the comment section.
If you don't have the needed skills, you can easily boost them via Skill Implants/Packages, gloves, belts, and headgear provided you have at least one skill point invested in each.]
When in conversation with T3-M4, and there is a line with either [Computer] and/or [Repair] in front of it, choose it. Remember to always be polite and, if your relevant skill is high enough, you should succeed. Do this repeatedly until there is a final choice indicated by [Computer/Repair]. Once this succeeds, you will have learned Moving Meditation and gotten this achievement. Along the way, both you and T3 will have increased a number of your attributes too, so it's a good idea to do this regardless of the achievement.
Any questions or suggestions to improve this solution are welcomed. Please don't leave a negative response unless you explain why you think that way and how I can improve this.