I’m not sure this is a bug or just an oversight but in The Dig mission using the laser drill to destroy the temples that hold the Xel’Naga relics count as killing enemy units for the new anniversary achievement, so you can’t go for both the achivement and the research points.
You can. You just need to do twice. So first round always do your achievements, then the rematch you can do your research. It has been this way since the original achievements haha.
Or just make a save right before the drill kills the temple, and reload it to grab the relics once you’ve gotten the achievement