All regular achievements can be achieved by just playing through the regular game. The game is not hard, and there are very few places where you can get yourself killed. It's mostly about making choices, which is up to you on how to deal with.
There are two achievements you might not get (but still possible) in your first playthrough. If you want to get this all in one playthrough, I suggest playing the chapter with Wyatt last, since that's the achievement that has a random element to it.
Reunited - An easy one. Start the Russell campaign and walk forward. As soon as the car gets close, you have the option to hide or stay put. Hide. That's it.
Two out of Three - Start the Wyatt campaign and play any way you like, until you have to decide who leaves the car to check out the body. Agree to play RPS and well... just win. It's all random, and it's a 1/3 chance each time. There is no strategy for this, other than you being lucky. If you win 2 out of 3 hands, you win.