Here is the full list of all 26 Samurai Aces III: Sengoku Cannon achievements.
Watch the ending with Koyori
Stage 5 clear
Stage 4 clear
Clear the stage without destroying any enemies
Stage 3 clear
Stage 2 clear
Stage 1 clear
Upgrade the shot until maximum
Watch the ending with Junis
Watch the ending with Tengai
Watch the ending with Mizuka
Watch the ending with Ayin
Watch the ending with Masamitsu
Watch the ending without continuing in EASY mode
Watch the ending without continuing in NORMAL mode
Watch the ending without continuing in HARD mode
Collect maximum quantity of bomb
Increased life
Obtain more than 50 bonus items
Scored 1,000,000 with Junis
Scored 1,000,000 with Tengai
Scored 1,000,000 with Mizuka
Scored 1,000,000 with Koyori
Scored 1,000,000 with Ayin
Scored 1,000,000 with Masamitsu
Unlock all achievements