The Ancient Light is a hovering white orb of light that is absorbed into the body of those who touches it. Obtaining the Ancient Light allows the user to perform the Light Speed Attack, an attack that destroys multiple enemies at once.
In Sonic Adventure, the Ancient Light is located in the Mystic Ruins Adventure Field when Sonic has to proceed to Red Mountain. To obtain it, one has to go into the cave that appears in front of the train station in the Mystic Ruins and go through the tunnel, until Sonic gets to the other side. With Angel Island to the left, pass through the field until Sonic gets to the entrance to the bridge leading to Angel Island, and the Ancient Light will be located on a flat rock platform to the left of the bridge entrance. With it, Sonic is able to proceed onto Red Mountain Action Stage, by destroying the Baby Kiki guarding it.
Sonic Adventure 2
Sonic the Hedgehog
Sonic can find his Ancient Light in Green Forest, which serves as an optional upgrade. After the second time Sonic needs to swing on vines and after coming through the second loop (half loop), he has to hit the springs and land on the desired platform. Once on this platform, go to the right and there will be a 10 rings Item Box. Go to the nearest edge and a Mono Beetle should appear, and use a series of Homing Attacks on it and the Item Boxes that appear behind it to reach another platform, where the Ancient Light is located.
Shadow the Hedgehog
Shadow can find his Ancient Light in Sky Rail, which serves as an optional upgrade. Left from the first Chao Container, which is located on the platform to the left, before taking the first rocket up, is a line of Mono Beetles. One needs to use the Homing Attack on them until Shadow reaches the spring on the other side of the pillar, which leads up to the Ancient Light on top of it.
The Light Speed Attack in both Sonic Adventure and Sonic Adventure 2, is simply an upgrade that makes fighting groups of enemies easier, other than that it serves no purpose.
Albeit, it is non-optional in Sonic Adventure and must be obtained without going through the wall leading to Red Mountain without glitches.
It is the only upgrade in both games that does not appear attached on Sonic and Shadow's body.