Here is the full list of all 42 The Banner Saga: Factions achievements.
You finished your first battle!
You finished your fifth battle!
You finished your tenth battle!
You finished your twentieth battle!
You were victorious in battle for the first time!
You were victorious in battle for the fifth time!
You were victorious in battle for the tenth time!
You have reached a win streak of 3!
You have killed 10 with a single unit!
You have killed 25 with a single unit!
You finished your fiftieth battle!
You finished your hundredth battle!
You finished your two hundredth battle!
You finished your five hundredth battle!
You finished your thousandth battle!
You were victorious in battle for the twentieth time!
You were victorious in battle for the fiftieth time!
You were victorious in battle for the hundredth time!
You were victorious in battle for the two hundredth time!
You were victorious in battle for the five hundredth time!
You were victorious in battle for the thousandth time!
You achieved an Elo Rating of 1100!
You achieved an Elo Rating of 1200!
You achieved an Elo Rating of 1300!
You achieved an Elo Rating of 1400!
You achieved an Elo Rating of 1500!
You achieved an Elo Rating of 1600!
You achieved an Elo Rating of 1700!
You achieved an Elo Rating of 1800!
You achieved an Elo Rating of 2000!
You achieved an Elo Rating of 2200!
You achieved an Elo Rating of 2300!
You achieved an Elo Rating of 2400!
You achieved an Elo Rating of 2500!
You have reached a win streak of 10!
You have reached a win streak of 25!
You have reached a win streak of 50!
You have reached a win streak of 100!
You have killed 50 with a single unit!
You have killed 100 with a single unit!
You have killed 250 with a single unit!
You have killed 1000 with a single unit!