Every Bullet Counts
Defeat Tatsuo without restocking your ammunition from the UAVs, on normal or hard difficulty
This fight is at the end of Chapter 4. The easiest way to go about this fight is utilizing your overlay to shoot at Tatsuo and avoiding him otherwise whenever you need to let your overlay recharge. As the achievement says, do not restock your ammunition (aka do not breach) the floating UAVs during the fight. If you run out of ammo, just pick up any of the guns dropped by enemies before and during the boss fight. If you are careful and use timed shots and shoot only during overlay, though, you shouldn't have to even change guns.
Shocking - 10
Kill 3 or more enemies from the electricity discharge of a dying electro armor unit
Best unlocked on Chapter 19 in the outside area (the one you enter by forcing that door-like thing open with X towards the beginning). When you see the flashy lights appear towards the garage-like doors, stand before it and ready your gun. These garage doors should open after you've killed the guys originally in the area and after you've killed the guys who come in by the dropships. When the garage door opens (should be the middle one), use your overlay and breach the blue-like man in the middle. Kill him ASAP, and his electric armor should discharge and kill the other guys that had spawned with him.
Greed is Good 35
Achieve CEO ranking on all chapters which track difficulty, on hard difficulty
CEO ranking is marked at the end of every chapter to the right during the chapter summary screen (seen at the end of every chapter). It is also marked as a checkmark on your chapter select menu if you have achieved CEO ranking on those chapters in the past.
CEO ranking is graded off of several things, but really, all you need to get high scores in are in accuracy (headshots help especially) and in breach spikes. Rampages can also boost up your score. While the CEO ranking does grade you based off of completion time, damage taken, and more, they really don't seem to have as much of a bearing on your final score as opposed to what I have mentioned above.
To get the achievement, you need CEO ranking in the following chapters:
Chapter 1 - Wakeup Call
Chapter 2 - Assault on Aspari
Chapter 3 - Aspari Extraction
Chapter 4 - A Train to Catch
Chapter 5 - Escape from Los Angeles
Chapter 7 - Voyeur Central
Chapter 8 - Cayman Global
Chapter 10 - Behind the Scenes
Chapter 11 - Ramon
Chapter 13 - Betrayed
Chapter 14 - The Wall
Chapter 15 - Kris
Chapter 17 - Corporate War
Chapter 18 - Spire Access
Chapter 19 - Burning Tower
Shield Breaker 10
Successfully sprint tackle 25 riot shield units
Many reports have shown that while the achievement claims you must tackle them, using a riot lance or electron mace on shield users in coop also works (coop riot shields can't be tackled).
Complete all Co-Op maps on any difficulty
Complete all 9 co-op maps. They are fairly easy on normal, even with randoms. You will start with Western Europe, and with each map completed, you unlock the next map.
High Value Asset - 25
Complete all Co-Op maps on expert difficulty
This one will be a little rough. On Expert, all of the spawns are overhauled, all of the enemies are tougher and dish out more damage, and usually bring weapons that hit harder. The main issues for most players will be guarding UGVs and agent battles. Gackt made a helpful guide for dealing with agent battles: LINK
Initial Public Offering
Be a member of a Syndicate consisting of at least 4 people
A "Syndicate" is a themed term for "clan". Join any Syndicate with four members (even if you are the fourth) for this to pop for everyone in the Syndicate.
Hostile Takeover - 10
Defeat an enemy agent squad
An "agent squad" is a group of four agents. They appear at the ends of Atlantic Accelerator, Scandinavia, and New England. Atlantic is the first level in the line of progression, so you will get it on that level if you're playing in order. It'll pop at the end of the level once they are all dead.
Save a team member that is stunned by an electron mace
You will need a partner to do this. When in Colorado or Scandinavia, have your partner get trapped by someone using an electron mace. Kill the sergeant with the electron mace while your ally is stunned. Easy!
Super Soldier - 10
Complete a mission without going down
This is easier as you level up solo, but is way easier if you have team mates healing you. Western Europe on normal should be a snap for this. Go slowly if you're a low rank, and work with a partner that you can trust will heal you. It will pop at the end of the level.
Highly Adaptable - 10
Kill 4 enemies in 4 different ways within 1 minute
This must be done in coop mode (you can be in a game by yourself, however). There are several methods to killing people, despite a loadout of only two weapons by default:
Takedown (RS near basic enemy type)
Also, it's possible to pick up another weapon, kill someone with it, rinse, repeat. Four in a minute should be possible at many parts of the game in single player and coop. Load up Western Europe. Kill an enemy with your main weapon, pistol sidearm, and melee. Then grenade the last. It'll pop after the 4th kill.