Here is the full list of all 8 Ludoria achievements.
Win your first battle against a wild Ludorom
Win 15 battles against wild Ludoroms
Win 30 battles against wild Ludoroms
Build your first base
Explore a distance of 1000 units
Explore a distance of 3000 units
Explore a distance of 5000 units
Capture at least 8 Ludoroms