The way to get the best ending can be seen here under the cheat called "Get Best Possible Game Endings"

Below are the other endings you should aim for once you've done that!

Alternate #1

Pyrrhic Victory: Rescue Woods.
Celerium: Retrieve the Celerium Worm.
Old Wounds: Kill Kravchenko with no resistance.
Time And Fate: Find intel and then search the compound throughly.
Fallen Angel: Find info on Zhao's secret meeting. Harper's face also gets burnt.
Karma: Karma doesn't die.
Suffer With Me: Menendez manipulates Woods. Woods dies and then SDC is left vulnerable.
Achilles' Veil: Try to shoot Menendez. Farid dies.
Odysseus: Admiral Briggs dies, then the USS Obama has no defenses against the enemy assault. The USS Obama's crew is killed.
Cordis Die: Save the President.
Judgment Day: Capture Menendez.


Alternate #2

Pyrrhic Victory: Rescue Woods.
Celerium: Retrieve the Celerium Worm.
Old Wounds: Kill Kravchenko with no resistance.
Time And Fate: Find intel and then search the compound throughly.
Fallen Angel: Find info on Zhao's secret meeting. Harper's face also gets burnt.
Karma: Karma dies.
Suffer With Me: Menendez manipulates Woods. Woods dies and then SDC is left vulnerable.
Achilles' Veil: Try to shoot Menendez. Farid dies.
Odysseus: Admiral Briggs dies, then the USS Obama has no defenses against the enemy assault. The USS Obama's crew is killed.
Cordis Die: Save the President.
Judgment Day: Kill Menendez.

Alternate #3 (most call this the worst ending!)

Pyrrhic Victory: Woods dies.
Celerium: Retrieve the Celerium Worm.
Old Wounds: Kill Kravchenko with no resistance.
Time And Fate: Search the compound throughly.
Fallen Angel: Find info on Zhao's secret meeting. Harper's face also gets burnt.
Karma: Karma dies.
Suffer With Me: Menendez manipulates Woods. SDC is left vulnerable.
Achilles' Veil: Save Faird and try to shoot Menendez.
Odysseus: Admiral Briggs dies, then the USS Obama has no defenses against the enemy assault.
Cordis Die: Save the President.
Judgment Day: Kill Menendez.