Would it be possible for a player to obtain a monster cohort? Monsters such as; troll, Barghest, giant, etc.
Yes, monsters can be cohorts as long as the GM approves. The bestiary lists Ettin as available at level 15, Stone Giant at level 18.
The Bestiary is pretty adamant that it is only OK with GM approval (and no leadership feat allowed at all in PFS games).
Hope this link works -
Go to Monster Cohorts
That is fantastic! Is there a specific formula, that you know of/ can find, to determine the level? Looking at the list, it doesn't go off of level.
I'm afraid to say there is no Rules As Written formula by Paizo to translate monster CR & abilities into what availability level you can have non-standard cohorts at the present time.
The list is a bit confusing and contradictory since it was cobbled together between three bestiaries and Pathfinder Player Companion: Knights of the Inner Sea. I can't speculate if that means there is no formula used, or if there was a formula not available to the players as of yet.
This is one of those times in which a GM must make the house rule call until they print "Pathfinder Companion: Beast cohorts" or something similar.
Sorry I can't be of any more help to you. Anything more would just be my speculation on the matter, and it seems you desire something more canonical and mechanical.
(My personal speculation - it seems that the more intelligent and humanoid a creature is, the higher it's value as a cohort).