If you're new to Rogue Legacy 2, a quick introduction on what Scars are.

As soon as you beat your first boss (doesn't matter which one) a house will appear on the Docks: the Drift House. In it, you will find an NPC on the left called Geras. Talking to him will allow you to enter Scars.

Scars are (hard) challenges that will test your combat and platforming skills. They will reward you with trophies and Souls based on your performance.

At first, most of the Scars are locked and cannot be found.
Once you meet their specific condition though, they will appear somewhere in the castle as a red memory. Reading that memory (by interacting with it) will make the challenge available in the Drift House. Note that Aesop's Tome isn't necessary for that.

                                                   
                                            A Scar's red memory.

There are 16 Scars in total, with the first one available from the start. Called Mending Erebus, it will give you a lore explanation of what Scars are, and will track the trophies obtained in the 15 other ones.

This guide focuses on finding the Scars, and won't give any help clearing the actual challenges.
I'll try to keep it as spoiler-free as possible and will start with vague hints before giving the direct, detailed answer so that players of all kind can use it.

The direct answers always come with a video showing how to reach the Scars' red memories. If you don't care about hints, and/or don't want to read, here's the full 15 videos playlist:
https://youtube.com/playlist?list=PLl_kIyartWBzD8DgEmSMUXknNvCH2XR1m

This is the list of Scars & Dreams as it first appears. Jump to each Scar or Dream further in the guide to have more info.
To avoid spoilers, I'm leaving the names out, and will use numbers instead.

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Enter the Mending Erebus Scar, navigate to the 2nd room. You'll find the Red Memory right next to Geras. Interact with it to collect it.

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Enter the Mending Erebus Scar. Navigate to the 2nd room to the fireplace and use a spell or talent to break the nearby trick wall. Enter the hidden area until you reach the red memory inside.

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The red memory is in the very first room of the Citadel (the one you start every run in). It's too high to be interacted with normally. You need either of these 3 things:
- the Ranger's talent Ivy Canopy
- the Pirate's talent Pirate Ship
- an heir with Gigantism

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In Axis Mundi, the 2nd biome, reach the middle room, the one at the base of the Sun Tower. You will find the Pizza Mundi store. Enter it. Behind the props on the far left, you will see a crack in the wall. Stand there and press the use button (no prompt) to enter a hidden room. The red memory is there ready to be collected.

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In the Kerguelen Plateau, look for the Far Shores. A long room usually to the far right of the biome, with a teleporter in it. It's the room you found the Aether's Wings (double jump) heirloom. Navigate to the right of the room until you reach the big heirloom statue. Behind it, at the bottom of the rocky islet, is a trick wall. Use a spell or talent to break it. Inside the newly opened passage, press use to enter the hidden area, then navigate to the bottom of it to find the red memory.

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One lore room in Study comes with a set of 3 doors. The middle one, protected by void walls, leads to a big room full of journals. Right after entering it, head straight to the far left and stand in front of the barrel there. Press the use button to enter a hidden room. The red memory will be there ready to be collected.

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Head over to the Pishon Dry Lake, and find a special room spawning there: the Storage Room. Enter it and don't break any prop.
Read the right sign at the top. It will have a crude map with arrows for different sections. Look at the arrow for the Accessories, and note where the tip of the arrow points to.
Stand exactly on that spot (one of the barrel) and press use (no prompt) to enter Tubal's hidden workshop. Once there, head in the top right corner and you'll find a banner. Break the trick wall next to it to reveal a secret passage. Entering it leads to a secret room containing the red memory.

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Head to the Stygian Study. In a long room containing a teleporter always on the left side of the biome, you'll find the portal to the Gong Head Sisters' fight. On the right side of the roof above it, accessible from outside, you'll have to use magic attacks (talents, spells or certain relics) to break a trick wall.
Head into the passage opened (might require a Vault rune to reach) and enter the hidden door. It leads to the Gong Head Sisters' study where you'll find the red memory ready to be collected.

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At the far right of Axis Mundi, right before the Boss' throne room, lies the Eastern Gatehouse. It's the big building with torches, lamp posts and two big water wheels.
Climb on its roof (might require Vault runes, or navigating to the rooftops of nearby buildings as it's pretty high). The red memory is on the right side.

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Head to Kerguelen Plateau, and look for a special room that look small and empty (it's flat and 2 room long).
On the right, break the trick wall leading to a hidden passage. Stand in the middle of it and press use to enter a secret doorway. The room it leads to contains the red memory ready to be collected.

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Head to the eastern ramparts in the Stygian Study. It's a long room on the right side of the biome leading outside. Cross the chasm to reach Enoch's Observatory. Press use until the platform inside it are visible. Get to the telescope platform and fall directly under it. You will land on a hidden platform. Walk left until you see an interact prompt, and use it. You will enter a hidden room with the red memory ready to be collected.

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In the Citadel, look for a unique chamber, a tall room with 9 hanging lamps. On its left wall, break open the trick wall using a magic attack (spells, talents or certain relics). Enter the door in the hidden passage.
Climb the tower it leads to all the way to the top. The red memory sits on top of the right rampart ready to be collected.

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First of all, before you can look for the red memory, you must not have killed more than one Boss. If you've already done so, resetting/changing threads is necessary.
If you haven't, then head to the Pishon Dry Lake, and look for the Nibiru Deep room, a special room at the bottom of the biome containing a teleporter.
This room has a huge drop in the middle and water at the bottom. On the bottom left of that drop, there's a trick wall that you need magic attacks (spells, talents or certain relics) to destroy. Doing so will open a passage with a hidden door inside. Enter it to find the red memory waiting to be collected.
Note that the water level at the bottom of the room rises with each boss killed, which explains why it's important not to have killed more than one of them. It's still possible, albeit pretty hard, to get to the memory if you've killed 2 bosses, but any more than that and it's out of reach until you change thread.

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Head to the Kerguelen Plateau, and specifically to the Far Shores, a special room on the far right. It's the room that contained the Aether's Wings (double jump) heirloom.
In the middle of the room, protruding out of the water, is a small rocky islet. The red memory will be sitting on it, ready to be collected.

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Head to the tutorial area. You can access it when changing/resetting threads. After the first indoor part, you'll have to use spin kicks to climb a tall building. Do so but instead of continuing right, keep climbing to the top of the wall and then jump on the left until you reach the roof of the previous building (you may have to use double jumps and/or dashes runes).
In the middle of the rooftop lies a small campfire. Walk there and drop down under it into a hidden area. Navigate the passage until you reach a door on the right. Enter it and explore the big room it leads to until you find the red memory for the last Scar.

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Head to the Pishon Dry Lake area, specifically, the throne room. Near the entrance, opposite the Dragon, you'll find half-hidden in a corner, a binding stone similar to those encountered in the ending sequence after beating Cain.
Keep the interact button pressed while near it, and the purple Dream memory will start going up from the ground to your right. Do so until it's just about above the ground so you can interact with it and unlock it.

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Head to the Axis Mundi area. In the teleporter area, in the top right, is a door leading to the tower that housed the Echo's Boots heirloom. Enter it.
Climb that tower until you reach a dead soldier on the left side. Partially hidden behind him is a binding stone, like the one you used during the escape sequence after Cain's fight.
Keep the interact button pressed while near it, and the purple Dream memory, as well as a platform to reach it, will descend to your top left. Once the platform stop descending, quickly dash and jump around it to reach the memory.

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Head to the Citadel Agartha area. Look for Lamech's secret chamber. Its entrance is hidden on the left wall of the Tower of Lights, a room that contains 9 breakable lanterns.
Once inside that area, look for the room containing training dummies and weapons displayed. Hidden on the right behind breakables is a binding stone, like the one you used during the ending sequence, after beating Cain.
Keep the interact button pressed while near it, and the purple Dream memory will start rising. Once it's above the ground, interact with it to unlock the Dream.