Bastion

There are 23 vigils in the game, which are "collected" at the Memorial. You will clear quite a few of these with natural story progression, but a few require specific feats with certain weapons. For this achievement, you must complete and claim 12 vigils at the Memorial in total. You get an onscreen note each time you complete a vigil and they will have a red star over them at the Memorial for you to "claim" them, which will turn them gold and reward you. I will provide a list below and hints for the tougher ones:

1. The Valediction - Construct a Memorial to Caelondia.
This one is automatic, as you cannot claim vigils until you construct this building.

2. The Dynasty - Earn First Prize in the required number of Proving Grounds (you need seven first prize wins out of the eleven available in the game).
This might take some practice, but upgrading the weapons to max makes the challenges much easier to complete.
Fang repeater is a cakewalk with the fully upgraded weapon.
Cael Hammer needs 30 seconds or less, so it is fast.
Duel Pistols requires 700+ points. Faster shooting each target nets more points.
Brusher's Pike can be ran through with an upgraded weapon, and you can move through some turrets with damage to save time.
Bullhead Shield is not too hard once you get your timing down.

3. The Culture - Gain a required number of Mementos.
Can be found on the lands and can be bought in Lost & Found

4. The Service - Learn at least 20 Secret Skills.
As you progress, you will unlock new skills for each weapon, and have new ones available at the "Lost and Found" to buy.

5. The Country - Restore 13,000 pieces of land.
This will come with natural story progression, as you are always restoring land when enter new territories for the story.

6. The Mercy - Defeat 15 different foes.
This is another story-related one. The final enemy is the rock chicken thing (not sure of the name). But it is the white bird that drops rocks from the sky.

7. The Masons - (Cael Hammer) Deal 70 damage with one blow to a single foe.
This should come from an upgraded hammer with focus on damage. You can get it more easily by hitting bosses with multiple swings until you get a slam or uppercut.

8. The Breakers - (Breaker's Bow) Defeat 3 foes with one shot.
Utilize the Power Shot on a cluster of enemies, or several lined up in a row

9. The Trappers - (Fang Repeater) Defeat a foe with the last bullet.
This should happen automatically, but squirts make an easy target for this.

10. The Menders - (Bullhead Shield) Defeat a foe with a melee counter when you are under 20% health.
To counter, you get a notification on screen when you use to counter an attack and reflect damage back. Again, squirts are a great target for this one, as they have little health and do little damage with melee attacks.

11. The Gravers - (War Machete) Achieve 15 hits in a row without getting hurt.
Surprise, go for squirts again! They die easy, but you can get this by just being mobile when using the Machete.

12. The Marshals - (Scrap Musket) Defeat 10 foes at once.
Seriously, squirts. Just let them cluster up, then unload on a group.

13. The Slingers - (Dueling Pistols) Achieve 12 hits in a row.
Just take your time and aim before firing. Rapid firing decreases accuracy.

14. The Brushers - (Brusher's Pike) Stab, then throw the pike at the same foe and hit it.
Easiest to do on a stationary target, such as a turret enemy.

15. The Triggers - (Army Carbine) Get a kill with a Power Shot at a very long distance.
Find a stationary enemy, such as a turret, then keep your line of sight on them and back up until they are on the edge of the screen. Then center the shot and take a Power Shot to kill it.

16. The Cinders - (Flame Bellows) Defeat 20 foes with one blow.
Back to the quirts again! This is another cluster kill, ass one blow is one continuous usage of the Bellows (one fuel charge).

17. The Skippers - (Galleon Mortar) Inflict 999 damage with one shot.
Best achieved with a Power Shot on a group of enemies at a distance. Just be patient and line up your shot on a cluster of immobile targets. This is not for inflicting 999 damage on one enemy with a single hit.

18. The Mancers - (Calamity Cannon) defeat 3 foes with a single shell.
Given the power of this weapon, this should be no challenge. However, you can always upgrade it for more damage and splash damage.

19. The Inspiration - Upgrade 5 weapons to level 3.
Pick your favorite five and make them better.

20. The City - Spend 10.000.
Another natural story progression one.

21. The Conscience - Reach level 5.
Another natural story progression one, as you gain experience with each kill.

22. The Sanctuary - Build and upgrade every structure in the Bastion.
Another natural story progression one. There are six buildings, and you will upgrade each one.

23. The Faith - Complete a "Trial of the Gods," which is a Trip to Who Knows Where with at least 1 god activated.
I recommend Pyth as your god, as this should come automatically after you encounter the shrine in the story. If not, then activate Pyth and go through the Pipe, as that one is easiest and fastest trial.

If I am missing anything or you have suggestions, feel free to leave them in the comments, and I will edit this guide with credit.