This trophy can either be a massive pain in your back, or it can be another short grind for you. It depends on when you choose to start grinding for it. A specialization is the last upgrade in a path on the skill tree and is meant to be a great skill to get, which means you'll only be able to have one active at a time on a character. Its cost is the same as a normal skill, however, so you only need 6 skill points to get a specialization.

With this in mind, the best thing you could possibly do is to aim for one specialization with your first character while not upgrading anything else. Once you get that first specialization, you can move onto the second character, and once you set a different active specialization for that second character, this trophy will pop.

If you play through the entire game with only one character, this trophy can become more troublesome. If you still haven't completed 25 side-missions, you could do those with your second character, netting in a bunch of XP from those missions. Completing a mission awards 1000 xp, and additionally, destroying a relay beacon nets you 1,500 XP. With this in mind, levelling up shouldn't be as bad, but if you're all out of options, the best thing you can do is to join someone who just started the game and help with their missions. This will still award xp for you.

The chest in a safe house can be used by all your characters, and all content within is saved across all of them, meaning you can put all your guns inside, and use them with your second character.

Important Note: It is absolutely critical that you choose DIFFERENT specializations for your characters, otherwise you'll have to play a third time to try it again.