How do I stop my loft bed from wobbling?

That sounds like the frame is racking, meaning the rectangular sides are shifting out of square. Diagonal bracing is usually the direct fix. A plywood panel secured across the back, or diagonal braces across the frame, can resist that sideways movement much better than adding small corner brackets alone.

Put the bracing where it can connect several parts of the frame, and use fasteners suited to the wood and loads. Since it’s an elevated bed, don’t use it until the frame feels stable under careful testing.

A plywood panel can do a lot without making the whole thing look like a cage. Fasten a panel across the back of the lower section, and add one on a side too if the bed still moves in that direction. The panel needs to be firmly attached to the frame, not just tacked on in a few spots.

If you want to keep it open, use diagonal braces instead. A brace only on one face may not stop movement in every direction, so check how it behaves from the sides as well.

Before changing the structure, check whether all four feet are actually bearing on the floor. Floors can be uneven, and a bed can rock because one leg is slightly unloaded. A proper, solid shim under a foot may fix that kind of rocking, but it won’t solve a frame that sways when pushed.

I’d be cautious about extending a leg or fastening the bed to the wall just to pull it into place. If you anchor it, connect a solid part of the bed to wall studs with suitable hardware, and don’t use the wall connection as a substitute for sound bracing.

Also inspect the joints and fasteners. Loose connections can make even a braced frame feel sloppy, so snug them up and check for splitting or movement where the rails meet the legs. If the joints themselves are shallow or loose, reinforcing those connections may help, but don’t deepen notches without checking how much wood would remain. Cutting more can weaken a leg or rail.

For a tall bed, I’d favor adding diagonal or panel bracing and making sure the joints are secure, rather than relying on a deeper notch alone.