Here is the full list of all 23 Total War Battles: SHOGUN achievements.
Destroy a building using a Cannon.
Complete the first chapter.
Kill 5 or more enemy units with the same Samurai unit.
Deploy an elite unit.
Complete a side level in the campaign.
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.
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.