The achievement states "Build every Improvement in your home system" but what does it mean by "every". Some improvements are not possible as they require a planet type that may not be in your home system.
Is this possible for example if your home system does not have an asteroid belt - as without that you can't build a "Deep Space Facility"?
Also do you also need to build an "Invulnerable Empire" improvement?
I see that you've already found your answer on the Amplitude forums, but I'm posting it here for the sake of completeness.
To get the Holy Terra achievement you need only to build every improvement that is possible to build in your current home system. If your home system does not have an asteroid belt, you do not have to build a Deep Space Facility. If it does have an asteroid belt, then a Deep Space Facility is required.