You will need to have progressed
in the story, then you will need to have taken your longboat out onto the river and attacked at least 5 monasteries to get enough raw materials/resources to upgrade your settlement to level 3. As you level up, the difficulty to attack monasteries goes up slightly too but the ones around your starting area, then around Grantesbridge and then into East Anglia are all easy enough even in early stages of the game.
*Potential spoilers ahead*
It only takes 3 settlement upgrades to go from level 1 to 2, choose any 3 that cost the least resources (I recommend the Assassins Bureau & the Hunters Hut, along with the obligatory Blacksmiths forge as the Hunter can start giving you rewards for animal kills/carcasses & the Assassin Bureau unlocks the Leap of Faith which helps the descent when synchronising Viewpoints).
Going from level 2 to level 3 requires a few 4 more huts which are all a bit more ‘expensive’ (in their use of resources) which is why you’ll need to have plundered a few monasteries... personally I’d ignore some of the newly-unlocked settlement tents that only add to Feast buffs, and concentrate on the few that add value such as the Stable (which is one of the cheaper upgrades), the Barracks (so you can create your Jomsviking and unlock the “It’s Alive” achievement, as posted here:
and I chose the Tattooist and the Shipbuilder so I could personalise myself and my transport!
When your settlement reaches level 3, achievement unlocks.