This is no different from The Walking Dead game by Telltale games, if you have played it you will know that all the trophies can not be missed and are gained just by playing through the story.
If this is your first Telltale game i will give a little more detail.
To get the Platinum trophy you need to have completed all the episodes of season 1 and like i stated none of them can be missed unless you do not buy all 6 episodes of course.
There are 6 episodes in total that are all available now as of the 17th of November, so that makes up 5 DLC after the first episode and you can either buy each episode individually via the PSN store or buy a season pass and get all episodes in one go which you do need to download on their own and then install them and the season pass does end up costing less than buying all the episodes/DLC on their own, especially when there are sales on. However there is also a physical copy out there and as of this date i found a copy for as low as £23.49 here http://www.gameseek.co.uk/pd/VideoGamesfy91cpabhz/%7BMW%7D
(Sorry i only have access to UK pricing
)Not interested in sales and purchasing information? Skip to Summary at the end of the solution.
There have been sales recently for the entire Telltale collection which included The Walking Dead seasons 1&2, Game of Thrones, The Wolf Among Us and Tales from the Borderlands all in one bundle. It was on sale for £30 but now is back up at £79.99. Game of Thrones season pass was also on sale for £9.99 and on disc it usually goes for roughly £24-£30 and even though i got it for £9.99 i would have happily paid the full price if i had the money at the time.
I can not say if i think you should wait for a sale or go for the collection as i do not know when or if they will do the same sales again and i have not played all games that come with it. What i can tell you is that both seasons 1&2 of The Walking Dead i thoroughly enjoyed and felt a strong emotional bond with the characters in the game like i have never felt before in any other game and i really enjoyed Game of Thrones also. They all have very similar mechanics but it is the story that you play these games for. As of this date there is not a physical copy for the collection.SUMMARY
So a summary is that to plat this game you need to either buy the full season on disc or download all 6 episodes via PSN whether you purchase a season pass or buy them individually is up to you but once you have all 6 episodes you can not miss any trophies in this game as they are all story related.
I hope this information helps, good luck and happy gaming to you all