Here is the full list of all 28 Warbands: Bushido achievements.
Win 5 battles without losing a single unit
Make 500 points of damage
Kill 50 enemies with melee units
Kill 3 enemies with one unit in a single combat
Kill 10 enemies with ranged units
Win battle without losing a single unit
Kill 10 enemies with melee units
Make 1000 points of damage
Make 3000 points of damage
Win 15 battles without losing a single unit
Win 10 battles with only one unit left
Win 50 battles with only one unit left
Win 100 battles with only one unit left
Use Hand of Destiny card 10 times
Use Hand of Destiny card 50 times
Use Hand of Destiny card 100 times
Complete the main campaign
Get 500 coins
Get 1000 coins
Get 5000 coins
Kill 50 enemies with ranged units
Kill 200 enemies with ranged units
Kill 5 enemies with one unit in a single combat
Kill 8 enemies with one unit in a single combat
Kill 200 enemies with melee units
Kill a 4WP unit or higher with peasant
Complete Cutthroats scenario on Insane difficulty
Complete Samurai scenario on Insane difficulty