How to access levels 25, 26 and 27 in Doom 64:

In a normal game of Doom 64, a player exits level 24 (No
Escape), and appears at level 28 (The Absolution).  Levels
25 (Cat and Mouse), 26 (Hardcore) and 27 (Playground) are
bypassed.

These three levels are special "secret" or "hidden" levels,
and may only be initially accessed through the use of
special level passwords, or through the use of the game's
Features menu (cheat-options menu).

For information on enabling the game's FEATURES menu, and
for details on all the cheat functions in Doom 64, access:
DoomCode: Doom cheat codes

For special, extended passwords that enable the game's
Features menu, access:
D64FCode: Passwords to enable Doom 64's cheat menu

For passwords that take you directly to any of these maps
(and let you play them at any skill level), access:
Doom 64 passwords to start with normal status on any map
or
Doom 64 passwords to start with maximum status on any map