On this page of our trophy guide to Mafia Definitive Edition, you can find a detailed description of unlocking the Not Taken In trophy. You get this trophy for resisting arrest by the Lost Heaven Police Department.
You need to start a 2-star police chase – two stars and handcuffs icon must appear above the mini-map and an example of this situation is shown in the picture. It can't be a 3-5 star chase, because the officers will try to shoot Tommy.
The easiest way to start a level 2 pursuit is to kill someone on the street (except a police officer).
Don't run away, just wait for the police to arrive. Also, hide your weapon so you don't provoke officers to shoot you.
Wait for one of the officers to handcuff Tommy. You have to respond to this by pressing the dodge key (ALT in the PC version). The main character will defend himself from getting arrested – this will unlock the achievement. You don't have to run away from the cops or kill them.