Command & Conquer: Red Alert 3

These objectives can be completed in any order or difficulty so don't panic if you miss one, simply replay the mission. From personal experience if they were obtained during co-op play and the achievement does not unlock try playing a single player mission completing any bonus objects and the achievement should unlock (thats how i got the closer).

Credit to Demon9Tom for the list:

Mission 1: Protect the Hermitage

After repelling the first wave from the fortress, you will be told to save the Hermitage. Use a Bullfrog parachute Natasha and some Flak Troopers over to eradicate the Rising Sun attacking the Building.

Mission 2: Rescue the Telsa Troopers

After Crossing the River head to the centre of the circus area to free up some bears, after saving the bears head north to find the first group of Telsa Troopers, kill the guarding Units to take command

Assist the Telsa Troopers:

After Freeing up the first squad of Telsa Troopers head back towards the launch facility to find the second squad, again kill the guarding units to take command of the squad.

Mission 3: Set up Base Defenses

After destroying the initial forward base and receiving a MCV both commanders need to build a sentry turret and flak gun (if playing alone the AI will do this automatically)

Destroy the Generators:

After the Battlefield expands a series of generators will be marked on your map, either use your recaptured dreadnoughts of a fleet of sicles to destroy them.

Mission 4: Capture the Swiss Banks

Note it is Capture not Destroy as destroying one fails the objective, there are six in total and AI capture of banks is allowed

Mission 5: Destroy the Tech Inhibitor

The Tech Inhibitor is located on the Island directly east of your base, the easiest way to destroy it is to use twin-blades as there is little anti air present.

Mission 6: Build an expansion base

After Krukov becomes your enemy you will be told to build an expansion base, build a sputnik and send it to the south western corner of the map with a couple of units as an escort, unpack the sputnik to complete the object

Mission 7: Destroy the Generators

After the map expands the location of these generators will be highlighted, send a largeish force to take care of them

Rescue the captured Bear and Conscript:

Again when the map expands their location will be marked on the map, regroup your forces and fight you way to north western area of the map as you approach the compound the objective will complete and the units fall under your control.

Mission 8: No Bonus Objectives

Mission 9: Capture the New York Stock Exchange

Once you gain control of your base build up some twin-blades and MIG's and destroy the forces guarding the NYSE, once the are is clear twin-blade an engineer across to capture it.

Eliminate Agent Tanya:

Tanya will be Highlighted as an objective so she won't be hard to find either go after her when your ready to destroy the allied base, hit her with a vacuum imploder or send an expendable unit i.e twin-blade to harass her so she comes over to fight you, making her an easy target.