There are a few items that are very useful and hard to find in Pokémon Mystery Dungeon DX Rescue Team, but the one that most players will want to find quickly is the Friend Bow.
This is a special item that not only increases the chances that wild Pokémon will want to join your rescue team after defeating them in a dungeon, it also includes recruiting Shiny Pokémon.
So for players who want to change the way they Shiny Hunt and try to recruit a few off-color team members, the Friend Bow is a must-have. All in all, this will increase your chances of recruiting by around 10%, which makes it a very worthwhile investment if you plan on trying to finish the postgame.
You won't be able to acquire the Friend Bow during your main part of the story, as it's only found in the post-game, but it's relatively easy to find compared to other in-game items.
While trying to find a "Mirage Pokémon" in a quest after completing the game, you will be prompted to enter Mt. Far and climb the dungeon on the 60th floor. On the way up, be sure to fully explore the 30th floor, as this is the first place you can find the Friend Bow - and the only one that won't cost you anything.
You can also go up an optional dungeon, Joyous Tower, but not only will you be reset to level 5 when you enter the tower, but it is also an item that you will have to purchase at random from a Kecleon store on your way up. If you choose to pellet it this way, make sure you can afford the 5000 PokéDollar prize or have the plan to escape the Kecleon Flood that will swarm around you if you try to steal the item.
Friend Bow at Far Mt. is your best bet for getting the item quickly, as he's already on his way to fight Ho-Oh, so you can also pick him up and equip him to your team leader to take advantage of the benefits of its effects.