This Air Necklace consists of a necklace-styled oxygen bottle that allows Knuckles to stay underwater for an unlimited amount of time without drowning. This eliminates Knuckles' need to search for air bubbles or the surface of the water to breathe. This upgrade is extremely useful during Knuckles' section of the Cannon's Core, which consists of very deep submerged passageways.
The Air Necklace upgrade is found in the Aquatic Mine, and is only accessible when the water level is at its minimum. Even after finding the entrance to its hiding spot, it is hard to reach since the passageway leading to it is completely submerged, maze-like, and ridden with spikes. It is also very dangerous to reach because there are no air pockets or bubbles until the end where the Air Necklace is located, greatly increasing the chances of the player drowning.
To reach the Air Necklace, the water level in the Aquatic Mine must first be reduced to its lowest level. This is done by heading up to the floor above the main room, by taking the upreel found on the top on the central square structure in the main room. Once there, touch the switch found in front of the sign that says "3" and the water level should be lowered.
With the water level lowered, head into the underwater brick room by going into the shaft found in the corner of the main room, and you will see the octagonal tunnel. Once you see it, dive underwater. On the bottom of the brick room head into the tunnel with the Dash Panel and it will lead to a room with several wooden 2-by-4s. Dive to the bottom on the left of the tunnel in this room, and you will find yourself in another brick room. Head then into the tunnel found in the brick room and you will arrive in a vertical tunnel. The Air Necklace can then be found on the top of this vertical tunnel in a dry room, which can be reached by surfacing from the tunnel. Try making it to the vertical tunnel very quickly so you don't run out of air.
It was later discarded by Sonic the Hedgehog when they were about engage Hunter in battle, as he preferred to travel "light". Knuckles then left it fully behind after he regained his lost powers from being exposed to the Master Emerald's energies.
This is the only one of Knuckles' upgrades in Sonic Adventure 2 and Sonic Adventure 2: Battle that does not have an equivalent with one of Rouge's upgrades.