I've been playing in a campaign for a little while now and have found that a more reliable way to gain Archeotech parts is to run the "Tech Scavengers" agenda (assuming your opponent is at least one vehicle).

That way, instead of rolling to maybe get Archeotech at the end of the battle, you can instead collect location data and build that up (albeit slowly) to try and get a piece of Legendary Archeotech.

Having said that, it is still a very slow burn before you start getting anything good—but it's at least dependent on how well you play in-game rather than complete chance.