Here is the full list of all 34 Narita Boy achievements.
Find the access to Taiyo Beam’s red symbol
Insert the ‘Uppercut’ power-up
Find and install Taiyo Beam’s code
Reach Trifurcation, at the portal of the Three Houses of the Trichroma
Insert the ‘Shoulder Bash’ power-up
Metamorphose into your animal form
Defeat the first end-of-level Boss
Get hold of the first floppy backup disk to restore the Creator’s lost Memory
Use the Transcriptor of Symbols and transcend for the first time
Penetrate the first Creator’s Totem
Insert the ‘dodge’ power-up
Wield the Techno Sword and become one with it to overthrow the Stallions
Reaching the Digital Kingdom is quite an achievement
Find and mount your Servo Horse
Transform yourself into Servobot
Find Taiyo Beam’s hidden room
Insert the ‘Downstab’ power-up
Equip the Floppy Board
Find the Floppy Disk on the Technocrats’ balcony in the Capital
Activate the digital path that will allow you to ascend the Summit
Find Ougai Rain’s hidden room
Find and install Ougai Rain’s code
Activate the Switch with HIM’s Holo-History
Insert the ‘Dashstab’ power-up
Find Johnny Heat’s hidden room
Defeat the Glove
Find and install Johnny Heat’s code
Find the access Techno Key to the Capital
Get back to the Technocrats’ terrace in the Capital
Transform yourself into Big Narita
Defeat HIM
Unlock all the Creator’s memories
Return to the 80s after saving the Digital Kingdom
Retrieve all the fragments of the Backup Floppy Disk