On this page of the game guide to Borderlands 2 you will find a detailed description of the side mission titled Assassinate the Assassins. This is one of the few side missions that you can begin during your first visit to the Sanctuary.
1) Bounty board
Three Horn Valley
2) Bandit camp/passage to Southpaw Steam & Power
Southpaw Steam & Power
3) Assassin Wot (first floor)
4) Assassin Oney (first floor)
5) Assassin Reeth (ground floor)
6) Assassin Rouf (first floor)
Approach the Bounty Board and accept the mission . Head to Three Horns Valley and to the Bandits (the entrance can be found in its eastern part), where inside a building you will find a passage to Southpaw Steam & Power . Right beside the entrance there's a Fast Travel, so if you've already been here before, you can save yourself some time. Follow the corridor and you will reach a big room from the above screenshot. Don't go down, instead get on the bridge on the left.
Approach the gate from the above screenshot , from behind which Assassin Wot and his Bandit guards will come out. Once you kill him (do it with a pistol of your choice for additional experience), he will drop Assassin's Orders which you should pick up.
Go to the next gate shown in the screenshot , where you will have to face Assassin Oney (you can get additional experience for finishing him off with a sniper rifle). By his corpse you will find another Assassin's Orders.
Head through the newly opened passage to the right of the gate, from which Oney came. Follow the corridor to a room with two gates, where Assassin Reeth is waiting for you (bonus for killing him with a melee attack). Pick up another ECHO Recorder and go through the door on the right side of the gates.
You will reach a room with the last gate and Assassin Rouf (killing him with a Shotgun will earn you more experience points). Picking up the ECHO Recorder from his corpse will end the mission which you can turn it in Sanctuary . To the right of the gate you can find as shortcut leading to the exit from this location.