Beat a stage without using projectiles.

Easiest of the 3 "without x" achievements. Do an early stage after having a better sword and remember not to throw stuff.

Beat a stage without dashing.

Most easily done in an early stage, i did it while doing no swords.

Beat a stage without using swords.

Most easily done in an early stage and an upgraded ranged weapon that pierces enemies, can be done at the same time as doing no dashes.

Make Corgi Jr. dizzy in the shop.

Very easy, just switch tabs from the shop to your loadout as fast as you can, until it pops. Takes a few switches.

Cheat in Moe Jr.'s challenge in stage 4-4.

What this means is that you have to kill all 3 choices he gives you. Most easily done using a spear. Kill one on the left, damage the other two choices so they die in one hit. dash attack while staying in the middle, to the right side to kill the right one and instantly turn around to kill the one in the middle where you're staying yourself. you got like 1-2 seconds before the 3rd choice becomes invincible.

Reach wave 50 in the Oni TV Show.

This one is one of the hardest ones to get right imo.
It is very much possible though, but you need a bit of luck i feel like.
I had always reached around wave 40 before i managed to get to 50, but when i got to 50, i got to 80 in the same try, since i wanted to know how far i could get.

The most Important part is getting your hands on some healing.
There are these mask artifacts that you can get, which are ideal for this. I had a small brown one and even got my hands on the 3rd stage fully red mask, which just had me healing up all the damage that i took while fighting.

getting an ultimate ability is also great, as you'll always get a high combo, which will heal you greatly after a wave and you get healing while killing stuff, because of the masks too. i was at 100% HP until pretty much wave 75.

Lastly, get a throwable weapon, that can pierce through enemies, to be able to quickly kill the guys who can disable your sword. My most prefered sword was the Ruby Sword. It's long and quick and doesn't drain any energy while attacking. Makes it very easy to hit many enemies at the same time.

Also you can just let the timer run out, if you don't want to pick any new weapon or item. I highly advise you to do so, if you got decent gear and fear that you may downgrade yourself, if you don't fully understand each weapon.

Reach a combo of 500.

The way i did this, was to search for a stage that has a ton of enemies at the same time and equip the feather item. (4 damage/4 stamina)

Take a lot of stamina boosting artifacts with you (also the one that makes combos last longer) and start throwing them until you get it. Its not as easy as it sounds, but should be managable by everyone, once they figure out the perfect spot. i sadly don't remember in which stage i did it.

Get an S-rank medal in every stage.

This is the hardest achievement in the game.
I can't tell you how to S rank every stage, but i can give a few hints on how to obtain S ranks in general.

To get an S rank, you need to beat a stage, without having taken more than 100 Damage. (100 exactly is fine, but i've never gotten an S on 101 damage or higher)

You also have to be decently quick in doing so, but usually time isn't a problem. I only had a single stage in which it seemed like i was too slow once.

And you need to have a high combo count. beating a stage on 50 damage taken, but only a 25 combo, will often not work. Try to get around 75 for a combo. At LEAST 50.

Some stages need better scores than others too, but as a rule of thumb these seem to be the points to get to get an S in general.

Fashionista
Sword Expert
Projectile Expert
Artifact Expert

All of these Achievements need you to get everything in each category.
This means: Buying Everything in the shop, getting all the chests in the levels, clearing the game to unlock the last items in the shop and beating the 50 Waves Oni TV show, because you get 3 items for clearing wave 50. (you get items for every 10 waves cleared, but the last one is 50, you can't get them on earlier drops)

Make absolutely sure that you Cleared wave 50, as the Oni achievement unlocks by only reaching wave 50 already.
So to get everything, you need to actually reach wave 51.

Buying everything just means farming carrots. There is items for Carrot farming, but by the time you get all S ranks, the 50 waves achievement and all the chest drops, you should have almost all the carrots needed anyway.

So how do you know, where to farm your missing chests?
If you click to the menu, while on the map, there is an Statistik tab. Scroll down that tab until you see chests in the menu. There is different types of chests and it shows you how many of which, you have collected in each world.

Now you just gotta go find them. You can pick your favorite stage and pretty much collect all the chests there, you only need to check if you're able to get the right size of chest in the level you're in.

I hope i covered all achievements that you could have trouble with. Many are self explanatory and i'm writing all this out of my memory after i've beaten everything, but i think i've covered everything that i had trouble with myself.

Happy Hunting!