What achievements are impossible without DLC purchases?
Solution 1:
The achievements guide at xbox360achievements.org shows only 3 that require DLC:
- All Cousins (80 G)
- All Presents (80 G)
- Astronomic Katamari (90 G)
Note that these are the only three achievements that say "Download stages ..." in their description, and they add up to the 250 that's standard for DLC.