How do you open it without damage?

Ok I have figured it out. The service manual says:

1. Top Cover Removal

1.1 Place the console on the bench with the

front facing toward you. On the rear of the

console and using finger pressure only,

press inward in the center of the rear panel

just below the edge of the top cover (2).

When you have pressed the rear panel in

approximately 1/4", lift upward on the top

cover and release the pressure on the rear

panel of the console. The finger in the center

of the top cover should be sitting on top of

the corresponding latch hole in the rear

panel. Once the center finger has cleared, lift

upward on the rear edge of the top cover

until the four tabs to the sides clear the

console rear panel.

1.2 Slide the top cover to the rear of the

console approximately 1/2". Lift off the top

cover.

It wasn't very clear to me. Basically, the top cover slides off the device through the rear (where the connections are). But it has 4 triangular "fingers" holding it in place. These fingers are butting flat side against the rear "wall" of the device (the plane where the connectors are located). They're thin (maybe a millimeter thick) but rather tall (5ish millimeters).

To open it, you're supposed to unhook them with finger force so that the top plate then slides off... I couldn't do it like they describe, I had to use all my spudgers and guitar pics to lift the rear of the top cover so that these triangular fingers cleared the back wall and then slide the cover off. I used the blue "iFixit Opening Tool - plastic prying levers" to slide under the top cover and then lift the top cover. While holding it lifted, I slid a pick in the space to prevent the triangular finger from butting against the wall again. When doing all four like that, I was able to unlock the top cover. Be careful because in the middle there is a tab going through a hood and if you lift this one you'll snap the hook: that one has to slide off.

It's a crappy design to say the least. But I managed to open it without snapping anything; I'm surprised how flexible and forgiving the plastic is even after 20 years...

Service manual and electronic schematics available here: https://archive.org/details/bose-321-sm