Here is the full list of all 23 Total War Battles: SHOGUN achievements.
Complete the first chapter.
Kill 5 or more enemy units with the same Samurai unit.
Complete a side level in the campaign.
Complete a skirmish battle in any difficulty.
Deploy an elite unit.
Purchase your first upgrade.
Complete a campaign level with a 3 star rating.
Achieve your first victory.
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.
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 all skirmish battles in Normal difficulty.
Complete all skirmish battles in Hard difficulty.
Complete all skirmish battles in Shogun difficulty.
Complete all challenges.