I'm really curious. Do you think it's possible to reach an achievement score of 10,000 without actually spending any credits at all? 

I've managed 8000 on an alt without spending & that is just from boosting and the activity of the account

It could be possible. 

It's possible, but was easier to do so in the past as there used to be an option to share on to FB for an extra 10-20 points per site achievement. There were also special seasonal quests (that were completely free) which also increased achievement scores.

It was possible when wall, floor and landscape achievement can be done by using just duckets