Unfortunatly yes there is an online trophy and the worst about it is you need an online pass.(which is quite expensive for a trophy that takes 5 minute including loading time, 9,99$ canadian)
There is 2 way to have an online pass.
First one is to buy a brand new game(which i doubt it is now possible due to the fact it was out in march 2013)
2nd way is in the Playstation Store(thats what i did). it is somewhat hidden, if you go in search for dlc you won't find it. The only way i found to buy one is to select the game god of war:ascencion(as if you wanted to buy it) and underneath it there is multiple options, pick the option network pass, it will bring you to the online pass that now you can buy.
Now to the actual way of unlocking this trophy(if you did buy an online pass)
From the main menu, when on single player option go right it will bring you to multiplayer option. Once in control of the caracter select a god to pledge allegiance, when they ask to test your might say yes(that is basic training)
Once completed it will ask you if you want to do advanced training, say no and then go to the circle to exit.
and then....POP goes the trophy, as easy as that.
i do not know if you buy god of war:ascencion from the store if it comes with the online pass and i guess that, if you have a friend that has the online pass that you could probably do this trophy from their playstation. if anyone can confirm any of those 2 options it would be really nice, i will update this solution with the info and credit to the person who confirms the info.
Update: RayvenMorrigana confirms that if you got the game digital the pass is included, here's is comment:
I can confirm if you have the game digitally the online pass is included, so you do not need to buy it separately if you bought the game via the PlayStation Store or if (like me) you got it through PlayStation Plus.