The Hyrule Forest Park in The Legend of Zelda: Tears of the Kingdom is an island, both on the surface and in the depths. This makes it a bit difficult to access the Lightroot below. Here’s how to reach it from the surface instead.
You won’t be able to reach this Lightroot from the depths at all, since the entire island is surrounded by walls underground. Instead, head southwest of Sepapa Shrine, along the Hyrule Castle Moat. There is a small cave entrance by the water that leads to the Chasm entrance. Drop down into the water (beware the fast currents) and enter the cave.
Jumping into the Chasm will drop you right on top of a giant Frox, so be prepared to either fight or run. In either case, the terrain in the depths of Hyrule Forest Park is pretty flat, so just head north and slightly east to find the Apapes Lightroot.
All Lightroots in Tears of the Kingdom correspond to Shrines on the surface. This means that, if you don’t have a Lightroot unlocked, you can still know exactly where it is based on the surface topology. In the case of Hyrule Forest Park, there is only one shrine on the surface of the island: Sepapa Shrine.
If you’ve already unlocked Sepapa Shrine, you can enter the map, hover your cursor over Sepapa Shrine, switch to the depths map, and drop a marker on that exact spot. This marks the location of Apapes Lightroot in the depths.