At first glance, this achievement should be straightforward to unlock. Complete all the games, and the achievement unlocks. However, by my own experience, and the experiences of others, this isn't as straightforward as it seems. I've seen the case where this achievement remains locked while the other achievements are unlocked. This case seems strange, especially in light that getting all the other achievements involves beating all of the games (or two or four times in the case of Bloodlines and III respectively).

The reason for this involves flags. The flags for all of the other achievements generally occur as soon as the final hit for the last boss is hit and the ending cutscene plays. The flag for the Heir to the Belmont Clan doesn't occur until during the credits, or possibly to the end of the credits. If the player quits out before hitting the flag, then this achievement will not pop until that flag is hit, creating the above problem.

Not all is lost, though, as players can go back into the game and trigger the flag by watching the ending credits for each respective game. Once all of the flags are hit, this achievement should pop. When should it be safe to quit out of the game? When the ending credits finish.

Castlevania I - When the game starts its second loop (Stage 18)
Castlevania II - When the game returns to the Press Start screen.
Castlevania III - When the game starts its second loop
S.Castlevania IV - When the game starts its second loop
Castlevania Adventure - When the games shows "Presented by Konami"
Castlevania Adventure II - When the game shows "End"
Castlevania Bloodlines - When the Konami screen appears
Kid Dracula - When the "End" screen appears.

Once all the flags are hit, the achievement should pop up. If it doesn't, then it means that the game was quit out of before hitting the flag. In that case, replay the end boss (hope you used save states!) and then let the credits play out.