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You don’t need to take the holder apart. Just twist the metal back off the AirTag to replace the battery; the AirTag can stay in the holder.

But if you do want to take it apart, remove the key ring and twist the two halves of the holder.
 
i have the same holder and it’s a turn mechanism. Just hold the back piece and turn the front piece and it should unlock and separate.
 
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You don’t need to take the holder apart. Just twist the metal back off the AirTag to replace the battery; the AirTag can stay in the holder.

But if you do want to take it apart, remove the key ring and twist the two halves of the holder.
The first part is the answer! The second part is really non-obvious: it just doesn't wanna budge either way. That's why people are asking. But, as the use case is probably to change the battery, knowing you don't need to do that is going to be good enough, most of the time.
 
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