The light world dungeons are set in order as are the first and last dark world dungeons. However, once you get the dark world you can just leave dungeons after getting the item and move to another one so technically you can "finish" numbered dungeons 1 through 7 in any order. I do that frequently since some bosses are really ridiculous (Skull Woods- dungeon 3 in the dark world for example). Assuming you just want to complete dungeons entirely in one visit, then there are significantly more restrictions than A Link between Worlds (although it's still a very open game).
The dark world items by dungeon number are:
1- magic hammer
2- hookshot
3- fire rod
4- titan's mitt
5- blue mail
6- cane of somaria
7- mirror shield
8- red mail
You want to get the titan's mitt ASAP because that unlocks dungeons 5 through 7 (although you need more items to beat them) as well as enables you to upgrade your sword. The blue mail would be my second priority but you need to do some prep work to beat its dungeon. Dungeon 5 also happens to be one of most confusing and lengthy dungeons in the game.
You are stuck going to dungeon 1 first in the dark world as you need the magic hammer to open up dungeons 2 through 4. Getting to 4 for the titan's mitt next will make the game easier as you can upgrade your sword. It's a little confusing how to get there in the dark world (and isn't easy to explain) but you have to enter a dark world portal near the southern entrance to the lost woods and it involves backtracking through the woods.
Next I would recommend going to 3 for the fire rod and leaving since level 5 which has the blue mail is an ice dungeon. 3 is a super nonlinear dungeon up through getting the fire rod so you don't lose much by just leaving without beating the boss (seriously I find the boss so annoying that I wait until I'm practically done with the game then beat it when I'm overpowered). You technically can beat 5 without the hookshot but I wouldn't recommend it for a first runthrough. So that means you might as well do 2 next as it isn't a horrible dungeon and it has one of the easier bosses.
The cane of somaria from 6 makes the hardest puzzle in the game which is in dungeon 5 a joke (it's a multi-floor block puzzle to press a switch whereas the cane of somaria lets you just make a block to put on the switch out of thin air). Also 6 is one of the easiest dungeons in my opinion. It's very nonlinear though so it's daunting at first to figure out what to do, but it also has an easy boss.
Dungeon 7 can technically be done before 2 or 5 but there's little benefit to doing so as it is a tough dungeon and the mirror shield is helpful but not worth skipping around for in my opinion. Finally 8 opens once 1 through 7 are complete so it's last.
So I would say 1, 4, 2/3, 6, 5, 7, 8 is easiest. I would finish 3's boss before or after 7. Dungeons 5, 7, and 8 are definitely the most difficult in my opinion. The bosses in 3 and 7 are the two most difficult in my opinion as well. On subsequent playthroughs you can learn how to get through 5 and 6 without the hookshot, but I wouldn't recommend it on a first playthrough.
Also here are the rules for the dungeon orders (assuming you beat dungeons in a single visit).
1 is always first
2 must be after 1. What's unique is that 2 can be completed 2nd through 7th because the hookshot turns out to be optional in places where it seems like it's needed (tricky to beat 5 and 6 without the hookshot though- 5 requires a more complex path through the dungeon and 6 you just need to know how to turn the backwards recoil of running into a block with the Pegasus boots into a jump across a chasm in the first room). Other dungeons are more rigid in their potential completion order because of dependencies on items found in other dungeons.
3 must be after 1
4 must be after 1
5 must be after 1 and 4 and is virtually impossible before 3 (I've heard that you can use the bombos medallion instead of the fire rod but that's making the game much much harder) and easier after beating 2
6 must be after 1 and 4 and it seems like you need to beat 2 but with a simple trick explained above the hookshot is totally optional here and not that helpful.
7 must be after 1, 3, 4, and 6.
8 must be last
