Bastion

TLDR: Mortar, Fire Bellows. Roll, use fire, roll, use mortar, rinse & repeat! ;)

Access this particular dream by selecting the History Books in the Bastion. This particular dream only appears in New Game Plus (or Score Attack Mode) and sits just southwest of the Monument, to the left of the Stockpot. It was added as free DLC in the XB360 game.
It consists of 30 waves of all types of enemies.

Glitch? (personally untested): It is apparently possible to use the Battering Ram to complete this dream. If you go through the last level and get to the end [Turn on all 10 idols before starting the last level], choose to pick up Zulf and carry him back. Then when you get to the Bastion, select the History Books and you will enter the Stranger's Dream with only the Battering Ram active. Since there are a number of ranged enemies here I'm not sure if this is a good idea or not but it may be worth a try considering how powerful the Ram is. If you find it too hard with the Ram and you're playing in Score Attack Mode, just finish the game, then click Continue and you'll be back at the Bastion with your regular equipment and you can try it normally.

First off, do this on your 2nd playthrough in Score Attack Mode since that's when you should be worrying about maxing out your level and weapons anyways.
You should be at least lvl 7 before you try this. It's possible earlier, but why torture yourself.

Before I begin, let me preface with this: I've had some questions asked about why I haven't incorporated tips for every single wave (Reflection) or why I have similar solutions for each dream. The reason for this is that you use the same exact method to deal with almost every enemy in the game when using the loadout below (exclusions will be listed in Tips section). Slow them with fire and shoot a mortar at them.
I will provide a few specific tips below for particularly harmful enemies/rounds if deemed necessary or if people comment with questions about specific waves.

Weapons
Galleon Mortar
- Rapid Bombs
- Target System
- High-Explosive Charges
- Dampened Tubing
- Immunity to Bomb Damage (The most important)

Fire Bellows
- Sustainable Fuel
- Napalm Reservoir
- Modified Intake (THE most important tool you'll have. This slows down foes dramatically which makes fast moving enemies much easier to deal with using the Galleon Mortar)
- Contoured Grip OR Shielded Grip (Whichever you prefer)
- Industrial Furnace (Important for range purposes. And since you have the Napalm Resevoir and Modified Intake, just hit them a bit, then roll and use the G. Mortar to finish them off)

Distillery drinks
(I will list the 7 most important ones, then options for 8,9, and 10) :
1) Leechade (THE most important since enemies won't drop health tonics with all idols on)
2) Bastion Bourbon
3) Black Rye
4) Lifewine (You have no idea how useful this is. I was skeptical of it at first but it's literally a lifesaver)
5) Bull Brandy OR Cham-Pain if you don't mind the side-effect
6) Hearty Punch
7) Werewhiskey (This is really important if you still have a few Reflections left but you're out of health tonics. You start doing massive damage at low health which helps you gain back health really fast with Leechade)
8) Bull Brandy OR Cham-Pain (whichever you didn't choose before)
9) Whale Ale
10) Graver Gimlet

Secret Skill
Turret Surprise
(This is extremely useful because besides damaging enemies it also serves as a great distraction and it lasts for a long while if you can help it keep alive. Also, if you've failed a specific round (Reflection) multiple times and find it to be the hardest one, just drop down 2 turrets instead of one)

Tips
Dream Specific:
- There is a "hiding" spot on the far right side of the map. It's behind the 3 stalagmites (pointed cone-shaped rocks). Go on the right side of these rocks (it looks like you're almost falling off the edge). From here you can safely launch your Mortar. Note: some enemies may still be able to reach you so be cautious when using this.
- This dream has tons of more conventional cover that appears over time. Use it constantly, especially to avoid the pincushions.

General:
-Roll......a lot.
-Try to use your Fire Bellows for like half a second to slow down fast moving enemies, then roll out of the way and drop a mortar on their face.
-For squirts, peckers, and stinkeyes, just spray flames all over the places then roll far away and repeat. Don't try to target one individually, your Napalm Reservoir will work it's magic on them over time.

One last tip that can be a huge game changer but is time consuming and/or tricky to pull off:
If you're not at level 10 yet and you're having a very difficult time with a certain dream, get yourself somewhat close to lvling up then enter the dream. If you time it right and can lvl up somewhere near the last 7 reflections or so, then all your health, health tonics, and black tonics will all be restored. This is especially useful for this dream since it is 30 Reflections instead of 20.

If I missed anything or you have any questions please let me know.

For the people who, like me, prefer visual aid...

Below a clip which helped me get the achievement, using the same settings, weapons, and strategy.

(Credits to Lion X for his contribution on YouTube)

Any suggestions to improve this guide are welcome!

Thanks for voting thumbs up if this guide was useful.

Good luck!