That's actually what caused some of my curiosity/uncertainty actually. It does suggest it's awarded on a mission-by-mission basis, but I assume that the 'total play time' is what's caused the acquisition of tortoise (as 15/16 hours by mission 9 seems rather slow, albeit there is the acknowledgement that a lot of that could be spent in Mother Base, on Side Operations, or on simply exploring the open world, whereas 21 minutes for a single mission doesn't seem that bad). Either way though, it is a relief to see that they're in the game.
Tortoise rank is awarded for vehicle usage, not time completed. Not sure if total game time would affect your rank anyway but I assume not.
Chick: Codename awarded to newly awakened soldiers.
Chicken: Codename awarded to soldiers whose weapon of choice was the chicken hat.
Foxhound: Codename awarded to soldiers who repeatedly completed missions with perfect stealth, no kills.
Fox: Codename awarded to soldiers who repeatedly completed missions with stealth.
Eagle: Codename awarded to soldiers who used headshots to achieve great victories.
Puma: Codename awarded to soldiers who used hold-ups to achieve great victories.
Bear: Codename awarded to soldiers who used CQC (non-lethal) to achieve great victories.
Octopus: Codename awarded to soldiers who used non-lethal weapons to achieve great victories.
Mantis: Codename awarded to soldiers who used the knife to achieve great victories.
Bee: Codename awarded to soldiers who used handguns (lethal) to achieve great victories.
Scorpion: Codename awarded to soldiers who used submachine guns (lethal) to achieve great victories.
Piranha: Codename awarded to soldiers who used shotguns (lethal) to achieve great victories.
Doberman: Codename awarded to soldiers who used assault rifles (lethal) to achieve great victories.
Raven: Codename awarded to soldiers who used handheld and mounted machine guns to achieve great victories.
Wolf: Codename awarded to soldiers who used sniper rifles (lethal) to achieve great victories.
Shark: Codename awarded to soldiers who used handheld and mounted missile launchers to achieve great victories.
Orca: Codename awarded to soldiers who used throwing weapons (lethal) to achieve great victories.
Spider: Codename awarded to soldiers who used placed weapons (lethal) to achieve great victories.
Hog: Codename awarded to soldiers who used D-Horse to achieve great victories. Awarded to those with proven effectiveness working with D-Horse.
Tortoise: Codename awarded to soldiers who used vehicles to achieve great victories.
Hawk: Codename awarded to soldiers who used support helicopters to achieve great victories.
Whale: ?
Bat: Codename awarded to soldiers who were evenly skills in all arts of war.