Achievements
Marks of what you have done in the game, written to your account: each is earned once and stays when a world closes.
Where
Open the Settings menu and choose Achievements, just above My account; on the phone it is at the top of the Settings screen. It has no tab on the top strip, because achievements belong to your account, not to a world.
The top of the page shows the points you have earned and the total of all points. Below it the achievements sit in groups: the ones you have earned (newest first), the ones under way (closest to done first), the ones you have not earned yet, and the secret ones.
They belong to your account
An achievement is written to your account, not to your player. You earn it once, in whichever world it happens first; doing the same in another world does not give a second set of points. When a world closes, your achievements and points stay.
No achievement can be bought, and none depends on where you stand in the ranking. What they give is points and honour; they give no resources, strength or happiness in the game.
Points and progress
Each achievement shows its points on its row. Most are earned in one go. Some are counted, such as the plunder brought home from expeditions; their rows show a bar and how much is done.
The one tied to the daily gift asks you to complete the seven-day run of the Today's Gift. If you miss a day the run starts again, so this achievement's count starts again too.
Notices
When you earn an achievement, a line lands in Activity, and pressing it opens this page. If you are a Pro member a notification arrives too; you can switch it off under the Achievements topic.
The figures come from the game's own content. Balance updates can move some numbers; the rules themselves are as written here.