This can be missed in a normal run, but can still be achieved by using a level select password.
Usually you'd need to grab a key subweapon from an earlier level, rescue Annette's sister, then while you still have the key, open the alternate Level 5 exit door.
Or you can use the following password:
AXE, HEART, AXE
AXE, FIRE, AXE
HEART, HEART, FIRE
Play through alternate level 5, or 5' as the game denotes it until you get to a screen with a rising water timelimit. On the screen following this, you'll come to a flooded section with platforms you can't access yet, and a small stream of water pouring in from a column. Break that column with your whip and the water will drain, then follow the platforms to the bottom and exit to the left of the screen where Annette awaits for the trophy.