The Ravening Beast (10 Points)
Achievement Reward: Banner Shape (Tribal)
Kill Ghom on Normal Difficulty

Additional achievements for harder difficulties:
Nightmare (Banner Accent: Feelers)
Hell (Banner Pattern: Dark Lightning)
Inferno (Banner Sigil: Ghom)

Ghom is found in the Larder in Act 3.

Making a Breakthrough (10 Points)
Achievement Reward: Banner Shape (Stalwart)
Kill the Siegebreaker Assault Beast on Normal difficulty

Also:
Nightmare (Banner Accent: Crossed Scimitars)
Hell (Banner Pattern: Low Waves)
Infernal (Banner Sigil: Siegebreaker)

The Siegebreaker Assault Beast is a boss you fight in the Edge of the Abyss towards the middle of Act III.

A Question of Lust (10 Pts)
Achievement Reward: Banner Shape (Stately)
Kill Cyadea on Normal Difficulties

More Difficulties:
Nightmare (Banner Accent: Troubled Heart)
Hell (Banner Pattern: Large Hearts)
Inferno (Banner Sigil: Cyadea)

Cyadea is found inside the Sin Heart in the Tower of the Cursed in Act III.

The Lord of Sin (10)
Achievement Reward: Banner Shape (Fiery)
Kill Azmodan on Nightmare Difficulty

Additional difficulty achievements:
Nightmare (Banner Accent: Double Blade)
Hell (Banner Pattern: Argyle)
Inferno (Banner Sigil: Azmodan)

You will fight Azmodan at the end of Act III

A Smash Hit (10)
Destroy Azomdan's War Machines

Blood Ties (10)
Complete the Blood Ties event

This event starts inside the Barracks, a random dungeon in The Battlefields

Forged in Battle (10)
Complete the Forged in Battle event

Talk to Ironsmith Maldonado in the Keep Depths to get this event

Waiting for Reinforcements (10)
Complete the Waiting for Reinforcements Event

Talk to Captain Haile in Stonefort and help him, to complete this event.

Triage (10)
Complete the Triage Event

This even can happen randomly in The Battlefields area

Tide of Battle (10)
Complete the Tide of Battle event

Search for this event in The Battlefields zone

Blaze of Glory (10)
Complete the Blaze of Glory event

This event starts when you talk to Captain Haile in Rakkis Crossing

Crazy Climber (10)
Completed the Crazy Climber event

This event happens in Rakkis Crossing

O'er the Ramparts we Watched (10)
Explore the following areas on the walls of Bastion's Keep
Bastion's Keep Watchtower
The Armory
Bastion's Keep Stronghold
Skycrown Battlements
Stonefort
The Arreat Gate

Keep It Safe (10)
Explore the following areas below Bastion's Keep:
The Keep Depths Level 1
The Keep Depths Level 2
The Breach
The Keep Depths Level 3
The Larder

Slaughter Fields Five (10)
Explore the following areas within the Fields of Slaughter
Edge of the Abyss
Rakkis Crossing
Fields of Slaughter
The Bridge of Korsikk
The Battlefields

The Mouth of Hell (10)
Explore the following areas in Arreat Crater:
Arreat Crater Level 1, Tower of the Damned Level 1, Tower of the Damned Level 2, Heart of the Damned, Arreat Crater Level 2, Tower of the Cursed Level 1, Tower of the Cursed Level 2, Heart of the Cursed, The Core of Arreat, Heart of Sin

Oh, The Places You'll Go (10)
Achievement Rewards: Banner Sigil (Ballista)
IMPORTANT: These are random dungeons. To see in which area each of these dungeons spawn, read: Diablo III Act 3 Random Dungeons Guide
Caverns of Frost Level 1, Caverns of Frost Level 2, Icefall Caves Level 1, Fortified Bunker Level 1, The Barracks Level 2, Battlefield Stores Level 1, Battlefield Stores Level 2, The Foundry Level 1, The Foundry Level 2, Cryder's Outpost, The Forward Barracks, The Underbridge

Wanderer of Arreat (10)
Achievement Reward: Banner Accent (Grasping Claws)
Complete the Act II exploration achievements listed below:
O'er the Ramparts we Watched
Keep it Safe
Slaughter Fields Five
The Mouth of Hell
Oh, the Places You'll Go

Beastmaster of Arreat (10)
Achievement Rewards: Banner Sigil (Hare)
Read the following Bestiary Lore Books in Act III:
Blood Clan Khazra, Colossal Golgor, Demon Flyer, Demonic Hell Beaver, Demonic Tremor, Demonic Trooper, Herald of Pestileence, Hulking Phasebeast, Siegebreaker Assault Beast. Soul Ripper, Succubus, Tormented Stinger, Cydaea, the Maiden of Lust, Ghom, the Lord of Gluttony

Primary Sources (10)
Read the following people lore books in Act III
Bloodstained Letter
Ghom's Log
Journal of Hansan Haile, Captain
Leah's Journal Part 13
Leah's Journal Part 14
Leah's Journal Part 15
Leah's Journal Part 16
Morgan's Journal Part I
Morgan's Journal Part 2
Morgan's Journal Part 3

Espionage (10)
Read the following quest Lore Books in Act III:
Battlefield Reports
Orders from Azmodan, Part 1
Orders from Azmodan, Part 2
Orders from Azmodan, Part 3
Orders from Azmodan, Part 4
Orders from Azmodan, Part 5
Orders from Azmodan, Part 6

Historian of Arreat (10)
Read the following World Lore Books in Act III
Fall of the Barbarians, Part 1
Fall of the Barbarians, Part 2
Fall of the Barbarians, Part 3
Fall of the Barbarians, Part 4
Fall of the Barbarians, Part 5
The History of Bastion's Keep

The Wages of Sin (10)
Achievement Rewards: Banner Shape (Knightly)
Complete all quests in act III:
The Siege of Bastion's Keep
Turning the Tide
The Breached Keep
Tremors in the Stone
Machines of War
Siegebreaker
Heart of Sin