At the minimum you need one playthrough on Easy/Arcade for Lair King and one on Hard for Quest Complete.
Start out on easy/arcade and when you get to the dragon's lair save and complete it without losing a life then reload and do lair king. Then do your hard playthrough. In the process you should pick up everything else except the two secret achievements (which can be done in the first scene on a new game, Date With Daphne which can be unlocked by changing the system clock if you're so inclined and 1983 Mode (which can be done in one of your first two runs, or a third).
One run through without dying/reloading takes 12-15 minutes (ish).