The are a total of eight assassins that will be tracking you down throughout the game. You will encounter six of them through natural story progression. These are: Killer Croc, Deathstroke, Copperhead, Electrocutioner, Firefly and Bane. After a fairly simple, yet unique "boss battle" against them, you will subdue the assassin and GCPD will be contacted to pick them up.
The remaining two assassins, Deadshot and Shiva, are not related to the main storyline, however. You will have to initiate specific side missions in order capture them. Deadshot's side mission, which involves investigating an S.O.S signal in Bowery district, will become available after you deal with Copperhead inside the Steel Mill. Shiva's mission can be started right away after completing the story mission that takes place inside the Gotham Merchants Bank.
Both Deadshot and Shiva are also listed under your Most Wanted hub once their side missions begin. You can use their records in the Most Wanted hub in order to track your progress or see details pertaining to their mission. Once you have finally captured all eight assassins, the achievement will unlock.