Dust An Elysian Tail

This mostly involves spamming projectiles in combination with dust storm. They track enemies and hit many times to increase your combo quickly. Un-equip all your gear to do less damage and avoid killing monsters before hitting 1000. Getting hit and having your chain broken, even after surpassing 1000 hits, will NOT earn you the achievement.

This can be done very easily, very early in the game with these two giants.

If you're already past that part, you can also get it fairly easily on those monsters with funny mouths in chapter 2. You'll regularly run into big groups of them. My combo of choice is X, Y, B, down+Y.

Further still, in chapter 3 you'll constantly run into big groups of zombies which should also make a thousand hits easy. This video is at the very beginning of the chapter.

Go to Archer's Pass, but first, complete Chapter 2 to teach Fidget the Lightning Spell, and get the Ugly Pendant (should be in a treasure chest in the caverns if I'm not mistaken).
Now get to the first vertical right turn on the map (you'll see huge statues in the background), gather as many enemies as you can, stand in the corner and use B then Y repeadtly to power-up Lightning Storm after Lightning Storm, I climbed up to a 3000-something combo in a few seconds. Don't forget to run away before an enemy hits you and breaks your chain, or remove the pendant and re-equip all your highest power-ups to clean up the remaining foes.
If your stamina turns low or you turn red because of the Dust Storm, try to land a few hits with X to cool down, there's bound to be a blob in the group of foes, so if it gets too close between the electric shocks, try to counter him and hit him a bit to get some breathing space, however if you're around level 18/19 on Normal you should have little to no trouble. On Tough or Hardcore you might want to level up your Health, Defense and Fidget a tad more to play it safe, also stock up on food.

The trick here is that the Ugly Pendant divides your Attack, Defense and Fidget power by 10. So, if you remove all of your power-ups to keep your base attack, the pendant will only let you use a 10th of that (I have a base attack of 58 since I put some level gems in it, I only had 5 after equipping the pendant).

The video (not mine, btw.)will show you where to stand to get maximum efficiency, it suggests you spammed the Dust Storm, which can be a good strategy, but the Lightning Storm cranks up the hit count much faster.
Also, since you already leveled up quite a bit, you'll have some good gear as well to finish the job.

EDIT: Corrected the chapter number, and added a few clarifications and corrected typos.

Unlike "A Decent Start..." this one can be a little tricky to execute perfectly, but there is one area that you can perform a 1,000 hit combo perfectly. After you enter chapter 2 and obtain the fire upgrade for Fidget, you will be able to cast walls of fire which will fill the screen and chain together excessive amounts of hits.

The area in the video below is within the The Sorrowing Meadow. As you make your way down to the second mansion, you will have to deal with a phantom like enemy which you can only kill with projectiles. Have the phantom appear, but don't attack anyone, press "b" to fire a projectile, then press "y" to use the Dust Wind attack. Time your attacks, but once the wall of fire goes up, press "b" again and use your wind attack to chain a second fire attack.

Keep doing this and you will hit well over a 1,000 hit combo in this area. There are plenty of areas to earn this massive combo, but this is areas appears to be the easiest. If you happen to get hit, just jump back up and head back to the previous area and try again.

On easy mode, there is a much easier way to get this achievement, without needing combos or any other such move combination.

You need to get to chapter three, and have completed the four mansions in the story-based quest. I recommend doing the bottom-right mansion last, so you're near the save point for this achievement.

You'll want Fidget's electrical attack selected. Go up one room from the save point outside the bottom-right mansion in The Sorrowing Meadow, then go up one room. Now hold the B button, so that Fidget's electric attack is continuous. Just move up, through the room, by continuously jumping to avoid enemies, still holding B, until you get to two step-like cliff-hangs on the right side of the screen. You'll get a zombie-spawning phantom enemy attacking you, and there will also be a bug-spawning hive above you. Fidget's electric attack will home in on multiple enemies, causing your combo meter to start raising VERY quickly. Now just continue to hold B, continuing to use Fidget's electric attack, and continue just jumping above enemies until the achievement pops. My explanations aren't very good, so I've done a video to describe this method, which you can see below:

Here's how I got the Achievement; I'm sure there are other places you can get it too.

Head to the Sorrowing Meadow (graveyard) and visit the first of the four mansions for Cora. Now you'll have the wall jump and the choice of which mansion to visit next. Pick the Southeast one and make your way there. When you're two rooms north of the mansion entrance, you're in position.

Enter the room from the top - you'll see climbable walls on both sides, and to the left, a path with some spikes and a bug nest. Run past the bug nest and you'll encounter several zombies and a giant insect on the ground. Run just past them without fighting, and stop on the ledge while you wait for the enemies to approach.

Select Fidget's Lightning attack and start shocking the enemies who are following from the right. Once few if any remain, drop down and continue using lightning attacks on the many zombies below. Keep the shock going as long as you can, switching to melee attacks when Dust gets too red. Repeat this without missing or getting hit and you'll hit 1,000 before the room is cleared.

If you mess up, just exit from the top and start the process again. Also, if somehow you're killing everyone before you get 10K hits (which was not a problem for me), remove the augment you have equipped in order to reduce your attack power.

At the level with the graveyard, where wizards are generating zombies put on the ugly pendant and spam dust storm with fidgets fire projectile. You'll get it in no time, just be careful to stop for a moment when dust starts turning red.

I was able to use the slide kick to unlock this achievement with little trouble. Just group up around 10 or so enemies and just slide back and forth until you hit 1k then slide away.
It does 1 damage so no risk of killing off enemies before your done. You unlock the slide mid way through chapter 2.

One last note after you hit 1000 move away and let the combo end if you are hit you will have to do it again.

Note: Clear out all the bombs first.

Note 2: Also you will notice the combo nearly stops, IGNORE THAT, i have done this 3 times and every time got the same result

Note 3: This was done on easy and i'm not sure if it can be done on the harder difficulties, as you get hurt when you start to go red on Tough difficulty.

I've found the perfect place to do this in the Blackmoor Mountains, near the beginning there is a ledge you reach where you can hold down the button with Fidget's Lighting attack, will show it in the video, i have already got the achievement so it won't show it poppin but you will see the combo meter get well over a 1000.