Here is the full list of all 30 Shogun Showdown achievements.
Defeat Daisuke the Dasher
Defeat the Twins
Defeat Hideyoshi the Cunning
Defeat Nobunaga the Wicked
Defeat the Shogun
Defeat the Shogun on Day 2
Defeat the Shogun on Day 3
Defeat the Shogun on Day 4
Obtain the Swift Killer stamp with any hero
Obtain the Strategist stamp with any hero
Obtain the Combo Master stamp with any hero
Obtain the Obliteration stamp with any hero
Collect all Stamps with a single hero
Kill 3 enemies in a single turn
Kill 4 enemies in a single turn
Kill 5 enemies in a single turn
Kill an enemy from a distance of 8 cells
Deal 25 damage in a single attack
Have 40 enemies kill each other over the course of a single run
Accumulate 150 or more coins during a run
Upgrade a tile to the maximum level (level 8)
Defeat the Shogun with a deck containing only tiles with 7 or 8 cooldown
Defeat the Shogun with a deck containing only tiles with 0 or 1 cooldown
Defeat the Shogun without ever acquiring any new tiles
Kill a boss and die in the same turn