Spyro™ Reignited Trilogy

World: Ice Cavern
Triathlon
Defeat all three Ski Gnorcs

You will get this achievement naturally as you are finishing this level. These Ski Gnorcs are at the very end of the level. Below is an image of Ski Gnorc for reference.

World: Night Flight
Hot Wings 1
Flame all Fairies in Night Flight

Night Flight has total of 3 Fairies scattered around the map. I highly suggest doing this after you have finished level once so you have unlimited time to get the Fairies. Locations are as follows:

1. Just right of the cave exit after you have flown through five rings.
2. Fly past the third Golden chest after rings and a Fairy appears right in front of you.
3. The last Fairy is between the two lighthouses.

World: Doctor Shemp
What's in the Box?
Unlock the strong chest in Doctor Shemp

Just before the boss of this level, there is a hidden passage to the right protected by one big nasty Gnorc. Take her out. After that has been dealt with go into the vortex to get on top of the tower. After you are on top of the tower get the purple crystal from the left and from there glide towards your key.

The chest itself is right after you defeat Shemp. From there go close to the exit vortex and jump down to the chest which is on top of the big rock.

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World: Magic Crafters
Comin' Through!
Charge through 4 Armored Druids near the start of Magic Crafters

After you have rescued Cosmos there should be 4 Druids nicely lined up. Just place yourself in the corner and charge through them.

World: Alpine Ridge
Pops of the Tops
Detonate 3 explosive chests on the pillars in Alpine Ridge

After you reach the exit of Alpine Ridge next to it is a ledge from which you can glide into a hidden cave which has another dragon to rescue. You can either glide to the entrance or straight to the explosive chests. Just remember that after you flame your first explosive chest, start jumping to the next one as getting caught in the blast will knock you into the water.

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World: High Caves
Arachnophobe
Defeat all Metalback Spiders

Metalback Spiders can only be defeated by either a Super Charge Attack or a Super Flame Attack. There are total of five spiders. Two of them must be defeated with the Super Flame attack and three of them with the Super Charge Attack. A Fairy is located in the upper part of caves.

World: Wizard Peak
Egg Hunt
Defeat hidden Egg Thief in Wizard Peak

You will need to use a Super Charge to reach this place. When you get to the first Supercharge ramp in this level, use it and take a turn left. After that keep going onward till you see another Supercharge ramp, which is going the other way. Jump just a bit before you hit a wall and you should be able to charge right to that platform. The Egg Thief is hidden behind the wall on the platform.

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World: Glimmer
Hypersonic
Light 6 Gem Lamps in 15 seconds

Glimmer will be the first level you arrive into. After going past the exit portal there is a challenge giver next to a Superfly powerup. After accepting the challenge use the Superfly powerup. If you did not flame them in time you need to either die or re-enter the level. If you are struggling with this you could just come here in the postgame with Superflame (Infinite) powerup.

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World: Summer Forest

Well, You Might As Well
Complete Hunter's challenge

After finishing Glimmer, Hunter can be found to the right of the Idol Springs portal. He will give you the tutorial challenge for Glide and Hover. After finishing the tutorial, he will give you an Orb, and you will get the achievement.

World: Idol Springs

Bad Sushi
Do not feed the Hungry Idol any red fish

Before going for this achievement you must have purchased the Swimming ability from Moneybags for 500 gems in the Summer Forest. He is to the left of the Idol Springs portal.

Once you can swim, dive into the pond at the start of the level. Swim up the well that you should find underwater. After you jump out of the water, there should be Foreman Bud offering you a challenge.

You need to finish his first puzzle to move onto the next one. The puzzle is quite easy so you shouldn't have too much difficulty with it. Use picture 1 as reference. After you finish the first puzzle head back to the start of the level, where Foreman Bud relocated next to the Idol in the Water. Foreman asks you to feed 10 fishes to the Idol and for the achievement you need to make sure you don't feed red ones to the Idol. If you fail, simply retry this part.

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World: Colossus

Using Your Head
Charge a Goat in Colossus

After starting Colossus there should be some goats right away in front of you. Charge one of them for the achievement.

World: Sunny Beach

Rescued!
Headbutt every turtle in Turtle Soup challenges

In order to do this achievement you need to learn Climb first in the Autumn Plains from Moneybags for 400 gems.

After you have learned Climb, enter Sunny Beach again and get to the end of the level to start the challenge. For this achievement you must charge attack the turtles to the pond and not flame them!

You need to complete both Orb challenges to obtain the achievement.
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World: Aquaria Towers

Lockjaw
Destroy every Roboshark

Robosharks can only be defeated by the Superflame powerup. There is one at the start of the level. These sharks instakill you if you get too close, so you need to kill them from a distance.

World: Crush's Dungeon

Conservationist 1
Complete Crush's Dungeon without hitting any fodder

For this achievement you need to defeat Crush without killing any of the sheep that spawn during the fight. If you stay on full health for the entire boss fight, Crush wont spawn any fodder, which makes the achievement way easier.

As for the fight with Crush he is quite an easy one. As he runs from portal to portal just flame him from behind to do some damage. Blue portals will make Crush shoot waves at you which can be jumped over and the red portals will make him shoot fireballs at you which can be dodged by moving either left or right. After you have taken down Crush, the achievement should pop.

World: Ocean Speedway

Warm up the Crowd
Heat up the audience

Can be done at any point in the level. Just land into the audience and flame everyone except Queen Finny for the achievement to pop.

World: Autumn Plains
Long Distance
Complete the long glide to Orb in Autumn Plains

For this achievement you need to glide into the secret area at Autumn Plains (picture 3). I will explain how to get there in pictures below.

1. Just before the portal to the Gulp there is a cracked wall which you can charge through.
2. After continuing for a while you should come by an area with a vortex. Move into the vortex and it should send you to the top of the tower.
3. From there Glide to the secret area which you should see right in front of you.

World: Crystal Glacier

Bug Control
Defeat all Dracklets in one Superflight

For this achievement you must complete the Orb challenge of this level. If you touch the ground or walls it seems to count as a failure. To reset the count, simply kill yourself by jumping in the water.

World: Skelos Badlands

Unburnt
Don't touch the lava in Skelos Badlands

You might obtain this on your first trip to Skelos but if that was not the case just run straight to the exit on your second trip and make sure you do not touch the lava.

World: Zephyr

Gnot Cannon
Use a cannon to defeat a TNT thrower

TNT throwers are larger blue birds and there is only one you can actually shoot for this achievement. As you progress through this level you will come by a fairy and a turret. There is a doorway which you need to blast to progress. Blast it and shoot around the same area (shown in picture 1) to hit that pesky TNT thrower for an achievement.

World: Breeze Harbor

Trouble No More
Clean run in the trolley

Trouble with the trolley, eh? This used to be the most annoying Orb challenge in the original game, but it feels like they made this a bit easier in the Reignited Trilogy.

You need to collect 50 gears in the trolley area. See Autumn Plains world video for guide or check out the link I posted for it below.
(LINK HERE)

World: Scorch

Duck and Cover
Don't get hit by Bob

At the very end of the Scorch level you can find Handel next to a Superflame powerup which you will need during this, offering you an Orb challenge. Start it. After you take the Superflame powerup, backtrack to a flagpole and you should see Bob floating on top of it. Shoot him down and the challenge will start. His bombs are pretty easy to avoid so you should not have too much difficulty with this achievement.
Check out the video at the top of Autumn Plain sections if you want to see visual presentation of it.(LINK HERE)

World: Fracture Hills

Giantslayer
Defeat every Earthshaper in Fracture Hills

You can't do this achievement before you have learned Headbash from Moneybags for 1000 gems in Winter Tundra.

Only Hunter area giants need to be Headbashed while others can be defeated by charging them into lava.

World: Magma Cone

Ganked
Steal a Popcorn Crystal from Hunter

You can obtain this achievement from the Hunter challenge in Magma Cone. For the location of the Hunter challenge in this level see picture 1. Once there, you need to grab one of the Crystals just before Hunter is about to grab it. You don't need to finish the challenge to get this achievement.

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World: Shady Oasis

Dryfoot
Don't touch the hazardous water in Shady Oasis

This achievement is done the same way you did Unburnt in Skelos Badlands. But this time it is water and looks kinda toxic to me. You are likely to get this on your first trip as this is way easier to avoid than the lava was in Skelos Badlands.

World: Gulp's Overlook

Conservationist 2
Complete Gulp's Overlook without harming fodder

First things first. You can cheese this fight later on by using your infinite Super Flame rewarded for 100% completion and have no problems whatsoever to get this achievement. If you want to do this right away, prepare to spend some time here.

This is the worst achievement in Spyro history. It is the same as Conservationist 1, but with way more things to watch out for and a boss that's a bit more unpredictable than the Crush was. Let's go over his abilities.

1. Gulp starts to chase you from time to time so he can jump on you and smash you. To avoid this one, charge either to left or right of him while he jumps.
2. The thing that makes this boss annoying is his lasers. He will only shoot a few at the start but as the fight progresses he will shoot more and more until it becomes a nuisance. Best way to avoid this ability is to switch direction from left to right when he fires so you can make his shots more predictable as Gulp always shoots ahead of you.

If you get these 2 parts right rest of the fight should be pretty easy.

World: Icy Speedway

Flyin' High
Defeat the Snowmobiles before defeating a Hang Glider

Kinda simple compared to the last one as you only need to defeat Snowmobiles before defeating Gliders. Picture below if you need confirmation of the target you need to aim for.

World: Metro Speedway

Bird is the Word
Flame the Pigeons first in Metro Speedway

As with the earlier one just flame up the pigeons before anything else. Picture below.

World: Winter Tundra
Yard Work
Headbash every rock in Winter Tundra

As you enter the level you should have more than enough gems to buy Headbash from Moneybags for 1000 gems.

If you do not, backtrack a bit to earlier levels and come back here after you have enough gems to buy the next ability. All of the rocks you need to Headbash are in the outer area of the Winter Tundra. None of them are inside the castle grounds.
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World: Mystic Marsh

Monkeying Around
Charge through every Monkey in Mystic Marsh

This needs to be done without changing the world in between. Wait until they stop attacking and charge after that. They are hanging by the trees. Look at picture below for reference.

World: Cloud Temples

Sheeples
Don't hit any Sheep in Cloud Temples

As you progress through the level you will come by some Sheep encased in stone. It is okay to get close to the sheep. This is pretty much the same as the Ratastic achievement from Spyro 1.