After you defeat Yaridovich and talk to the true Elder of Seaside Town, you can go north to Land's End.
Explore Land's End
Save at the Save Block, then jump onto the cannon. Wait for it to be pointing away from where you entered, then press the button to be launched to where the platform is moving up and down. Before you move on to the next area, jump onto the moving platform if you aren't on it already, then face north, and when the platform is at the highest point, run and jump north to find a hidden chest that contains a Red Essence. The chest is only slightly north of the moving platform. See below for a picture that shows the shadow of the moving platform and the hidden chest, to help understand the positioning of the chest.
Go northeast to the next area.
As before, jump onto the cannon and press the button when it's pointing away from where you entered the area. When you land in the pit at the top of the ledge, three Chows will pop out. If you don't want the treasures in this area, just jump out of the pit and go east to the next area. Otherwise, jump out of the pit and stand at the southwest edge of the pit, then jump straight up to reveal a hidden platform. Go back to the cannon and make it launch you onto the platform that you revealed. The platform will move beneath a moving chest. Watch the chest's shadow, and jump as soon as you're under it. If you miss, you have to go back to the cannon to be launched on the platform to make it move again. Before you go, if you want to get the hidden chest in this area, launch yourself onto the platform again, then jump onto the high ledge to the north. Then walk to the west corner of this high ledge, then jump straight up to reveal a hidden chest that contains a Croaka Cola/KeroKeroCola. Then go east to fall off of the high ledge, and keep going east to reach the next area.
This area has a bunch of Geckits launching themselves onto the platforms with cannons. If you want to avoid fighting the Geckits, wait for them to fall off of the platforms, then quickly jump across. If you fall off, you will need to go southeast to launch yourself with a cannon. Go to the northeast end of this high ledge to reach the next area.
Save at the Save Block. Go east, and jump on one of the two easternmost flowers. Jump from one flower to the other to find a hidden chest that contains a Frog Coin.
Get Optional Treasure
If you don't want to take a detour to get some optional treasures, skip to Land's End, Part 2 below. Otherwise, if you do want to take a detour to get some optional treasures, go east from the chest you just revealed (see above) to reach the next area, then go northwest until you see a hole in the wall that sometimes has a puff of smoke come out of it. Jump into the hole where the puff of smoke is coming out, and you'll fall into an underground passage.
Go through the passage, jumping over the Geckits if you want to avoid fighting them, and jump onto the wooden crates to jump and hit the treasure chest, which contains a Frog Coin. Continue through the passage, and you will see a Chow (mouse). From the mouse, go to the northeast wall, then go to the northwest corner. Jump to find a hidden chest that contains a Frog Coin. Then go southeast down the stairs, and then northeast to reach the next area.
Go along the path and you will see some Shy Aways flying around. Jump on the barrels to knock one down to the lower area. Then go southeast, hit the treasure chest to get a healing mushroom, and jump onto the spring.
Be very careful not to fall down below or you will end up in Kero Sewers and have to go back across the map to return to Land's End. Carefully jump southwest over the gaps and hit the chest to get Cricket Jam. You can now optionally take the Cricket Jam to Frogfucius to get 10 Frog Coins. To do so, go south from where you got the Cricket Jam until you are in the area with a spring in the middle. Jump on the spring to go back to the world map, then go to Tadpole Pond and give Frogfucius the Cricket Jam. Then make your way back to Land's End, and go to the area with with spinning flowers and a Save Block. (If you don't want to go to Frogfucius now, you might still want to use the spring down below and just use the map to get back to Land's End. It's faster than having to go all the way back through the hidden passage.)
Land's End, Part 2
Back in the area of Land's End with the spinning flowers and the Save Block, jump on the nearest spinning flower to be launched to the next ledge. Repeat the process until you reach the top. Then go northeast to the next area. You will land in front of a cloaked figure. You can talk to them to play the Sky Bridge minigame. If you don't feel like doing the minigame, you can just jump northwest across the blocks, and if you fall, go southeast and talk to the cloaked figure to be launched back up above to try again. (The cannon at the end is only used for the minigame.)
Sky Bridge Minigame
If you play the Sky Bridge minigame, you have to try to jump across the bridge of floating blocks while Bullet Bills shoot at you. Depending on the difficulty that you choose, the blocks may fall if you stand on them too long. The prizes are coins for Normal and and Special, and a Frog Coin for Expert. After you win, talk to the cloaked figure to get your winnings, and you'll be asked if you want to do the course again to double your winnings. If you succeed at that, you get the option to do it a third time, for four times the usual winnings.
Land's End Desert
After you cross the sky bridge and go northeast, you will land in a desert. You can save at the Save Block. Talk to the mouse and say Yes to get directions to Monstro Town. (If you say no, the mouse will leave without giving you directions.)
Note that in the desert area, you may sometimes see a cloud of smoke that runs away from you. If you can jump and hit it, you will enter a battle with "Formless", which you can only reveal by hitting with a Special attack. After you reveal it, you fight Mokura, which is weak against regular attacks.
From the desert Save Block, go east and you will see two whirlpools. There is no ant in either of these two whirlpools. You can either jump into a whirlpool or you can go northeast or northwest. Afterward, look for the whirlpool that has an ant popping out, and go into that whirlpool. If you approach the ant from behind, you may be able to avoid fighting. If you do fight the ant, keep an eye on the whirlpool that the ant was in, because it will shuffle around. Repeat this process, going down the ant's whirlpools, ignoring the north exit (which just leads to the dead end that gives "Land's End" its name) and you will reach an underground area.
Use the Save Block, then hit the chest to get an invincibility star. Quickly run northeast through several rooms before the star's effect wears off, and fall into the hole at the end to land in a room full of Geckits. If you have at least 400 coins, you can jump behind the crates in this room and talk to a hidden cloaked figure to buy another invincibility star. If you buy it, hit the chest to get the star, then jump back over the crates and hit all the Geckits before the star wears off. Whether you bought the star or not, go northeast to the next room. You will end up in Belome Temple.