Select Armour of Awe from Valencia at the Crossroads of /museum then open the Awe Passes shop. If you're a member, purchase the Legendary Awe Pass and the Armour of Awe Pass, otherwise, only get the Armour of Awe Pass. Members can access their quests from the AQW Legend button while non-members do it through the AQW Hero button.
The way this works is that enemies will drop Shards. Turning in the quest turns Shards into Fragments. Then, you merge Fragments into a Relic in your Hero or Legend merge shop. The Relic is used to merge the Cape, Helm, or Armour of Awe.
You can get to each boss quickly by selecting More Details from within your Legend or Hero section. I highly suggest completing all of them with a group.
"Cape of Awe"
Defeat Binky at /doomvault once.
Because of Binky's difficulty, you'll most likely need a group of people to help fight it too. Binky has numerous abilities, including stuns ranging from 5-21 seconds, Skill Lock, which stops one of your abilities from being used (try and bait this with the Mana Vamp awe enhancement, a scroll, or your least useful ability first), and Prophetic Vision, which reflects your damage to you (avoid this by pressing ESC). If you have the Hardcore Paragon Pet, accept its "A Single Rib" quest too.
"Pauldron of Awe"
Defeat Ultra Akriloth at /gravestrike 225 times (Shards only stack to 150).
Akriloth isn't difficult but has over 600k HP. For some reason, the member version of this quest is a daily so complete the non-mem (Hero) version instead, which you'll need an Armour of Awe Pass to access from the Awe Passes shop.
"Breastplate of Awe"
Defeat Carnax at /aqlesson 100 times.
This boss is not difficult.
"Vambrace of Awe"
Defeat Ultra Blood Titan at /bloodtitan 225 times (Shards only stack to 150).
This boss hits fairly hard and has almost 400k HP.
"Gauntlet of Awe"
Defeat Ultra Alteon at /alteonbattle. These shards don't have a 100% drop rate but you need 125 of them (they only stack to 100).
The Ultra Alteon at /ultraalteon is much more difficult so it's best to farm at /alteonbattle.
"Greaves of Awe"
Defeat Mutated Void Dragon at /bosschallenge. These shards don't have a 100% drop rate but you need 150 of them, which they do stack up to.
This boss hits very hard and has over 400k HP.