One method I've seen to approach this is the development of one-shot-record-multi-read-only devices made as indestructible as possible. Attempting to get into or influencing the device to alter it results in the destruction of the recording.
While it cannot prevent loss of the recording, which has its own implications, it can prevent tapering.
However, it may not be able to prevent deliberately staged events unless there was also some sort of precise location tracking that either was completely internal or is external and somehow unblockable and unspoofable in and of itself.
As mentioned in the comments: tamper-evident is almost always as good as tamper-proof for evidentiary purposes.