Thief:

As noted elsewhere, the thief is slightly less linear than the rest. This is because of the hookshot, obviously. The hookshot only takes you to places you can go without it, but sometimes you can get somewhere ahead of schedule or can bypass using a superbomb. It's not a great ability, but it's sometimes good. All of these shortcuts have been in the game since the initial release (v0.90).

LEVEL 6 (Mirror Shield!!! and Flippers!!! and 6th Tear)
Here's an interesting challenge, and a even a full video below. You can use the hookshot to get the Mirror Shield and Flippers and then beat Level 6 before you even step foot in Level 3, Level 4, or Level 5 in any time period. You can do this as soon as you get the hookshot, even if getting the hookshot is the first thing you do once you cross the river. It won't be easy, since you have to fight a one headed Fire Gleeok to get the Mirror Shield, Reflecting Wizzrobes to get the Flippers, and an advanced Patra to get the Tear. It is possible as is, but I recommend at least getting the Blue Armor in Optional 1 and Slash in the northwest first Class Dungeon before attempting this.
In the present, go to the Help Cave (house) at screen 67. Walk there or use the whistle warp. Go north three times, and hookshot across the river. Go east, then north, and keeping to the west go north again. Go east, which is the only way, and you'll see the other river. Then you want to go along the river north, west, and west, and find two wood signs across this river. The cave is occupied by an NPC who gives you a heart container piece so you might as well hookshot to that side. If you want money, head straight south for a rupee sitting out in the open and a burnable bush.
Hookshot across the river east of the large superbomb rock. Go east three times and south once for the entrance to Level 4 present, which you do not need to go into.
Now you have an option. You'll need four keys to get the Mirror Shield, but if you get four keys beforehand you can skip to the boss and the Mirror Shield. Three of the four keys in Level 6 will be easier after you get the Mirror Shield, especially if you don't have the Magic Shield yet. If you steal keys from Level 4, take the west path in the dungeon.
Go east two more times, and you'll see a shallow spot you can hookshot to that will let you go east, into the Wandering Islands and the path to Level 6.
Go south once, but don't continue, there's nothing there. Instead, go east twice, and then north, and into the time warp. Go back to the Islands in the past, when it was frozen. Go south four times and you'll be at Level 6-1 Past. You can go through that dungeon like normal and collect the Mirror Shield at the end. If you need help check the Dungeon Walkthrough.
Just like normal, after getting the Mirror Shield you want to go to the future to the swamp. Go north four times, and through the time warp to the future. Reflect the zora fireball onto the yellow shield, or hookshot across, and go south. Go south, west, west south south east south east north and into Level 6-2 Future. Beat the dungeon and collect the Flippers.
Now you can get back to the present day, and everything proceeds like normal for the third part. Swim your way north, and go north three more times to the time warp and into the present. Walk and swim your way south four times and into Level 6-3 Present. Beat the dungeon and collect the extra bombs, magic container, heart container, and Tear. Now you can proceed forward to Level 3.
Thief Special: The Mirror Shield and Flippers (27m) Youtube video of the best way to get these two items immediately after crossing the river and selecting thief. It includes stopping in level 4 on the way for some keys that are easier to get. This video doesn't even get the Magic Shield or the Wood Bow. The only thing done across the river prior to this video was reading what they say in the class area about the four classes.

LEVEL 4 (Ladder and Master Sword L1 and 4th Tear)
This starts the same as the above path to Level 6. In the present, go to the Help Cave (house) at screen 67. Go north three times, and hookshot across the river. Go east, then north, and now go north on the eastern half of the screen. You can get to 4-3 right away, but you'll need the Ladder in 4-1 first. Go into the warp and go to the past. Go east, east, south, east, north, across the river and west to get to the dungeon. See the dungeon walkthrough.
Level 4-2 is a little more interesting. You can use the hookshot to skip it entirely, but it means being stuck with the Magic Sword until you get to the third group of Class Dungeons, and the Master Sword L2 is not optional. There's also the two heart container pieces in the dungeon to consider. Either way, you need to get back to the warp, so go east south west north, west, west, and go into the warp.
If you want to go to Level 4-2, go into the future. Go east three times, and hookshot across the river. Go west and go into the dungeon in the future. Beat the dungeon, and the when you exit go east, hookshot across the river. Go west three times but on the third stay on the northern half of the screen, and go into the warp.
For Level 4-3 you want to be in the present. If you have the Bracelet, go east, if you don't, go south and on the western half of the screen go north and then go east. If you skipped Level 4-2 or want to get a heart container piece and money, go north and west twice. The cave is occupied by an NPC who gives you a heart container piece so you might as well hookshot to that side. If you want money, head straight south for a rupee sitting out in the open and a burnable bush. When you're ready hookshot to the north side of the river east of the bombable rock, and go east three times and south once. If you got the Master Sword L1 at the end of Level 4-2, you could also go east twice, use your sword on the tentacle to cross the river, then north west and south to get to the dungeon (shorter distance but no items).

LEVEL 5-2 (Large Wallet)
ALL OF LEVEL 5 IF YOU HAVE LADDER (Silver Arrows and Large Wallet and 5th Tear)
This is pretty far out of your way to get one item, but you can beat Level 5-2 as soon as you get the hookshot. You can get to the mountains from the Flatlands two different ways, and there are ways to hookshot past most of the lava in the caves and overworld. The first brings you through the caves, the second brings you quickly to the warp. You should take a quick look at the Mountain Caves section of the walkthrough, becauase there are a couple heart container pieces.
First option is in the past. Go to the Flatlands screen 51, which is two north from Level 3. Hookshot down, and enter the cave, which leads to the heart container piece seen on screen 61. Go back through the cave, now go up the ladder to the Mountain. Go east and into cave K. Follow the only path and exit cave J. The cave north this screen has some money, but generally climb north up the mountain, with a little weaving east and west, and you'll be at the screen with the time warp. Stay in the past.
Second option is the future. Go to the Flatlands screen 61, just north of Level 3 (and the warp zone destination). Hookshot across the lava to the north. Go north (if you get to the purple rupee, there's a bombable wall with money behind it) and west, and hookshot across the lava. Go north into the Mountain. Go north three times, and then hookshot further up. Go north twice and then east, and into the warp, and go to the past.
From the screen with the warp in the past 01, go east, then down the ladder south, (go east and there's a bombable spot with money) and south again and you'll be at the dungeon screen 22. Hookshot down and you can enter Level 5-1.
Although you can get to the switch for the statues, you will need the Ladder to beat this dungeon. If you have the Ladder, see the dungeon walkthrough for the normal way through. Otherwise, to get the switch do this. Start out by going west and north, and you can get the compass. Go north four more times, until you can't go north anymore.Go east and get the key in the block puzzle room. You can't reach any of the other doors, so don't try.Go south twice, and then east through the locked door. Go north twice, and then north again through the puzzle. Get the map in this room. Go east and get a key, go east again. Skip the passageway and go east a third time and south to get a key. Go back north and west, and go into the passageway. On the other side you can go north to get the heart container piece, and back south. Go south, then west through the locked door, and south again. Go east, and get a key. Go back west and go south and west through two locked doors. Hit this switch with your sword, and all the statues will be lowered. Probably should F6 here because you want to exit the dungeon. Or the way back is ENNEN-passageway-WWSSSWSSSE.
With the statues lowered, you can get to Level 5-2 and Level 5-3, although you can't even get past the third screen of 5-3 without the Ladder. So you'll go to Level 5-2 in the present, which you can beat to claim the Large Wallet. First step is getting back to the time warp. This is a little longer path, but easy to follow. Go west south east, get the heart container piece in the stairs. Next go east, south, and into cave I. Follow the long circuitous path through the cave, which ends at cave H. In the overworld, go north twice and east, and you'll be at the warp. Go into the warp and go to the present.
There are two ways to go. If you have a superbomb and want to unlock the Warp Zone to the Coin Cave go west south, hookshot down, south twice and climb north up the ladder. You have to go inside for it to unlock the shortcut, but you don't have to go anywhere or fight anything. Outside the Coin Cave, go south down the ladder and then back north, and hookshot to the sign. Go east twice, and you'll see the dungeon entrance with a sign next to it but wait. If you want a fairy cave, climb down the ladder south, go east and north, and you go back the same way. Hookshot your way up to the dungeon. If you don't have a superbomb, go east south and hookshot across, then go east south and that's the fairy cave, and then it's just south west and north and a hookshot to the dungeon.
Level 5-2 is a little cheap for the thief. If you don't mind leaving behind a heart container piece guarded by a Ghoma, you can leave the dungeon with three extra keys. You only get one extra key if you want the heart container piece. The Ghoma guards a lockblock, but you can bypass that whole section at warp B with the hookshot (or flippers). Check out the dungeon walkthough which mentions the thief. If you don't have a way to kill the Ghoma or you just want to leave behind the heart container piece, after you go through the first passageway A go north and west. Don't go through the locked door north and instead go south and hookshot your way across. You've bypassed four locked doors and a key, making three extra keys.

Skip Levels 3-1 and 3-2
These two dungeons have the Medium Wallet and Wood Arrows, but you could skip them if you had the Large Wallet and Silver Arrows. The thief can do this pretty easily, but don't forget there's four heart container pieces between the two dungeons. You need to get the ladder in Level 4-1 (see the first part of the Level 4 above). Then you need to go to the mountain, and you can beat 5-1 to get the Silver Arrows, and once you lower the statues you can beat 5-2 to get the Large Wallet. You now no longer need the items in Dungeons 3-1 and 3-2.

Skip Level 4-2
This starts the same as the above path to Level 4. Follow the instructions to get the Ladder in Level 4-1. Instead of going to 4-2, use the warp to go to the present. Go east if you have the Bracelet, or south then north on the western half of the screen and east. Go north west west, and hookshot across the river (there's a heart container piece in the cave and a red rupee and a burnable bush to the south). Go east three times, then south, and you've gotten around the tentacle that could only be killed by the Master Sword, and can skip Level 4-2. You're going to need the Master Sword L2 from the third set of Class Dungeons as soon as possible (which is after Level 5-1).

Little More
You can get a HCP in the past Flatlands 51 without going through the mountain caves (this is also one of the thief's secret entrances to the Mountin).
You can get a HCP in the present Jungle 07 without using a superbomb. This is on the path to skip ahead to Level 6.
There are a couple secret money caves you can visit early, but that's mostly it for the thief.

I hope this has been illuminating. It doesn't seem like the thief has many options, but they are there.

If you want to retun to the description of the four classes without giving away the item list, click here.

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