Here is the full list of all 21 Gekido Kintaro's Revenge achievements.
Complete "The Deathtoll Rising"
Complete "The Three Seals"
Complete "The Ancient Book"
Complete "Searching For Koji"
Complete "The Final Battle"
Collect 1st Relic
Collect 5 Relics
Collect 10 Relics
Collect 20 Relics
Collect 30 Relics
Collect 40 Relics
Survive 1st Stage
Survive 2nd Stage
Survive 3rd Stage
Survive 4th Stage
Survive 5th Stage
Survive 6th Stage
Survive 7th Stage
Survive 8th Stage
Survive 9th Stage
Survive 10th Stage