With over 400 Pokémon to find in Mystery Dungeon: Rescue Team DX, you might expect not all of them to be as straightforward as the standard way to recruit a Pokémon to your team. Some Pokémon can only be captured at certain times, or if you have certain items on you at that time. These are normally high value Pokémon that you really want to find room for in your camps.
Mew is one of those Pokémon, and there are a few things you need to do before you can recruit them. First, you will need to have beaten Kyorge in the Stormy Sea. A few days later, you will receive a letter informing you of the existence of the Buried Relic, a place where Mythical Pokémon are often found.
You will then need to speak to both Shadow and Shifty and both can be found on Pokémon Square. Once you've spoken to them, the Buried Relic dungeon will be available. After that comes a trio of fights that you will need to win the Buried Relic dungeon:
- Regirock - 15F
- Regice - 25F
- Registeel - 35F
Defeating the three will get you the music box. Now that you have the music box, you can start searching for Mew which will appear at a random level between B36F and B99F. After that, the usual rules apply. You'll want to land the final blow with your Rescue Team Leader, and even then there will be a small percentage chance that Mew will join you.
Keep in mind that you also need a camp for Mew and you will need to have purchased Final Island Camp to have any chance of recruiting this Pokémon.