Here is the full list of all 23 Total War Battles: SHOGUN achievements.
Deploy an elite unit.
Complete a side level in the campaign.
Complete a campaign level with a 3 star rating.
Achieve your first victory.
Purchase your first upgrade.
Complete the first chapter.
Complete the second chapter.
Complete the campaign.
Complete all the campaign levels.
Complete all the campaign levels with a 3 star rating.
Purchase all the upgrades for one building.
Kill 5 or more enemy units with the same Samurai unit.
Sneak through an enemy unit with a Ninja.
Spot 3 or more Ninja with the same Monk unit.
Promote the same unit twice using the Veteran order.
Move a Cannon into the enemy's base.
Destroy a building using a Cannon.
Complete a survival level as your general is being attacked.
Complete a skirmish battle in any difficulty.
Complete all skirmish battles in Normal difficulty.
Complete all skirmish battles in Hard difficulty.
Complete all skirmish battles in Shogun difficulty.
Complete all challenges.