Heroes of the Ages (10 Points)
Join a cooperative game

This one is easy to get. Just join ANY cooperative game (either a public one, or your friend's one) to unlock this achievement. The easiest way is just to join a public game. From the main menu, click on "Public Games" then choose what quest you want to play, and you will be automatically matched up with other players on the same quest.

Heroes of Circumstance (10 Points)
Join a public cooperative game

This can be done through the main character menu. Just click on "public games" and choose a quest you are on, and you will join one of the many public games going on with other players doing the same quest, and around your level. You can leave as soon as you have joined and gotten the achievement, but why not continue and do the quest? Could be faster and more fun doing it with others, so you might as well give it a try

Warriors of Sanctuary (10 Pts)
Join a 4 player cooperative game where everyone is a different class

This one might take a bit of time, to find a public game where everyone (including you) is a different class. But join enough four-player public games, and you're bound to find a party that meets these requirements.

Gotta Catch Them All (10 Pts)
Play Cooperative games with the following hero classes:
Barbarian
Demon Hunter
Monk
Witch Doctor
Wizard

Just keep joining cooperative games, and eventually you will get this pokemon-reference achievement.

Follow me Around
Teleport to another player by clicking on his or her banner

This banner remains in town while the player adventures. Click on it to instantly teleport to that player, and earn this achievement.

Achievements for killing elites (10 Points Each):
Elites are Champion (Blue), Rare (Yellow), or unique (Purple) monsters

Bloodletting - Kill 25 elite (champion, rare, or unique) enemies in cooperative games
Slaughterhouse - Kill 50 elite enemies
Due Decimation - Kill 100 elite enemies
Massacre of the Damned - Kill 500 elite monsters
The Culling of Hell - Kill 1,000 elites (Achievement Reward: Banner Accent - Crossbones)

Life is Beautiful (10)
Heal other players for 500,000 Life by picking up health globes in coop games

The red health globes you pick up heal not only you, but your allies as well.

The Great Revival (10)
Resurrect a player of each class in cooperative games:
Demon Hunter
Monk
Barbarian
Wizard
Witch Doctor

Not Dead Yet (10)
Achievement Rewards: Banner Sigil (Death's Head)
Resurrect another player in a cooperative game

Breath of Life (10)
Resurrect other players 25 times in cooperative games

Savior of the Fallen (10)
Achievement Reward: Banner Accent (Skills and Banners)
Resurrect other players 50 times in co-operative games

For the above resurrection achievements, you can click on a player's gravestone to resurrect him or her, unless he or she have already resurrected at their last checkpoint.