Secret BFG 9000 in Doom 64 level 14, Eye of the Storm:

There is only 1 Secret on this map which will contribute
to the player's Secrets score: A BFG 9000.

Note that you must actually pick up this weapon in order to
be credited with discovering it (simply walking through its
location on the map will not affect your score).

From your starting position at the beginning of the level,
look for the 2 stairways that lead up out of the water, and
go up the right-most stairway.
At the top of the steps, bear right, and follow the path up
and around, until you find the elevated square hole in the
wall on your left, where the BFG sits.

Turn so that the BFG is on your right, and you're looking
back towards where you came from.  Follow the path back a
few paces, until you come to a yellowish square panel in
the wall on your right.  This wide square panel is divided
into 2 similar rectangular designs.

Walk up to the center of the right-hand design, and
Activate it like a switch (causing some bars to momentarily
rise up at the entrance of a passage below and behind you).
Immediately Run (remember your Run button) backwards, over
the wall behind you, to drop back down into the water
below.  Turn and run for the opening in the castle wall
before the bars drop down again.

Once you're past the bars, simply follow the passage up to
where the BFG sits.
If you can't take the BFG, it means you already have one,
and you also have maximum cell ammo.  In this case, simply
fire off some cell ammo (with a plasma rifle, laser or your
other BFG), and you'll be able to pick up this BFG, and get
credit for discovering this Secret.