A Vulture can be used to get Link onto the railing of a set of stairs near the Desert Palace entrance. To do so, stand in the corner made by the wall and the railing, and walk in the north-west direction when the Vulture attacks. Keep walking after taking damage, and when Link loses his invincibility, he will be pushed on the railing.
From there, it is possible to simply walk diagonally from the railing onto the brown ledge. Do not hug the left wall as you are trying to transfer over, because it won't work. Try to stand as far as you can in the top right corner of the railing, and walk directly towards the ledge. This part might take a few tries to get used to.
By using the Fire Rod to create a fire pillar in a corner near a ledge off which Link jumps, it is possible to get boosted similarly to a Bomb Boost. This can be used to get on top of the Desert area walls.
When entering the Hyrule desert area from the Lorule portal, you normally have to head south and climb 2 sets of stairs. From there you are supposed to go west and use the Sand Rod to make your way to different portals between Hyrule and Lorule. Instead of going west after climbing the stairs, you can merge the east wall and simply walk all the way to the right until you reach the area where you would have arrived by using the intended way.
In the east half of the Desert Area, it is possible to get on top of the walls surrounding the desert by luring a vulture into the right spot and damage boosting off of it. From there, you can simply walk to the southwest portal and then jump off the wall to it.
It is also possible to use a bomb boost to accomplish the same thing as the vulture damage boost seen above. This trick is very difficult and rarely used because of the convenience and ease of the other damage boosts.