This is the guide to getting 2 achievements.

Gaining a Foothold
To do: Complete 3 stronghold takeovers

After completing Story Mission 1 and 2, which commences automatically when you start a new game, you will be tasked with gaining trust for 3 different gangs. Each of them will be marked on your map with a different colour (Red, Blue, Yellow).
Each of the factions' first mission is a stronghold takeover, do all 3 of them to unlock this achievement.

Conqueror of Panau
To do: Complete 49 faction missions.

For every factions' stronghold takeover, certain areas of the map will be added to their territory. In this area you will be given a variety of faction missions. Complete all missions to obtain this achievement.

Conquering new areas by subsequent takeovers will add new missions to other areas of the map.The third bar on the map screen represents the amount of chaos needed to unlock more missions in the existing territories the factions have.

Note: Completed missions will disappear, which makes it very easy to track down the ones you haven't done yet.