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