Kill the Enderdragon.

Construct a better pickaxe.

Craft and place a sign.

Use a saddle to ride a pig, then have the pig get hurt from fall damage while riding it.

Catch and cook a fish!

Throw diamonds at another player.

Travel by minecart to a point at least 500m in a single direction from where you started.

Wear a full suit of Iron armour.

Use Shears to obtain wool from a sheep.

Attack and destroy a monster.

Construct one type of each tool (one pickaxe, one spade, one axe and one hoe).

Harvest some leather.

Use planks and sticks to make a hoe.