Successfully complete a single player game with the listed requirements to unlock the corresponding emblem.

Note:
You can get more than one in one playthrough, play through a few times to get more emblems, and because its such an awesome game (well done konami/hideo kojima)

Emblem	How to unlock
Ant	Shake 50 enemies for items.
Assassin	Kill more than 50 enemies with knife, have over 50 CQC holds, and get discovered less than 25 times.
Bear	Choke 100 enemies to death.
Bee	Use the Scanning Plug S or Syringe on 50 enemies.
Big Boss	Select the Boss Extreme difficulty, use no continues, get no alerts, kill no enemies (including Bosses), do not use the stealth suit or bandanna special items (can possess, but not activate), and have a completion time less than 5 hours.
Blue Bird	Give friendly soldiers 50 items.
Centipede	Get less than 75 alert phases, less than 250 kills, and over 25 continues.
Chicken	Get over 150 alert phases, over 500 kills, over 50 continues, use over 50 recovery items and complete the game in over 35 hours.
Cow	Activate over 100 alerts.
Crocodile	Have over 400 kills.
Eagle	Get 150 headshots.
Fox	Select the Naked Normal or higher difficulty setting, instigate no more than five alerts, kill no enemies (including Bosses), do not continue, do not use any life recovery items, do not use the stealth suit or bandanna special items (can possess, but not activate), and have a completion time less than 6 hours.
Fox Hound	Select the Big Boss Hard or higher difficulty setting, instigate no more than three alerts, kill no enemies (including Bosses), do not continue, do not use any life recovery items, do not use the stealth suit or bandanna special items (can possess, but not activate), and have a completion time less than 5 hours and 30 minutes.
Frog	Dive or roll 200 times.
Gecko	Press against walls for a total of 1 hour.
Giant Panda	Complete the game after 30 cumulative hours.
Gibbon	Hold up 50 enemies.
Hawk	Get admired by 25 friendly soldiers.
Hog	Get 10 combat highs.
Hound	Select the Naked Normal or higher difficulty setting, instigate no more than three alerts, kill no enemies (including Bosses), do not continue, do not use any life recovery items, do not use the stealth suit or bandanna special items (can possess, but not activate), and have a completion time less than 6 hours and 30 minutes.
Hyena	Pick up 400 dropped weapons.
Inch Worm	Crawl on the ground for a total of 1 hour.
Jaguar	Get over 76 alert phases, less than 250 kills, and less than 26 continues.
Leopard	Get over 76 alert phases, less than 250 kills, and at least 26 continues.
Little Gray	Collect all 69 weapons.
Lobster	Spend a total of 2.5 hours crouching.
Mantis	Use no continues, get no alerts, and have a completion time less than 5 hours.
Octopus	Get no alert phases.
Panther	Get over 76 alert phases, over 251 kills, and less than 26 continues.
Pig	Consume over 40 food items.
Pigeon	Have no kills.
Puma	Get over 76 alert phases, over 251 kills, and at least 26 continues.
Rabbit	Look at 100 Playboy pages.
Raven	Complete the game in less than five hours.
Scarab	Execute 100 dive rolls.
Scorpion	Have less than 75 alert phases, less than 251 kills, and less than 26 continues.
Spider	Have less than 75 alert phases, at least 251 kills, and at least 26 continues.
Tarantula	Have less than 75 alert phases, at least 251 kills, and less than 26 continues.
Tortoise	Hide inside a cardboard box or drum barrel for at least one hour.
Wolf	Have no continues and use no recover items.