Assassin is a type of combat racing event featured only in Jak X’s exhibition mode. It is similar to the Deathmatch event, in that you are pitted against other racers in a literal death match, except now you will be assigned one specific target to assassinate at a time, as indicated by the crosshairs superimposed on your target's avatar. The goal is to reach ten kills first or to have the most kills at the end of four minutes.
Note that while you are assigned a specific target, you and other racers can still target and kill anyone of choice. This can prove a constructive tactic if it appears someone has been assigned to you, or if you would simply like to clear someone off the field. However, killing a non-assigned racer will not reward you any points, and you should take care to reserve particularly useful weapons (such as the tracking missiles or Vulcan Fury) for point-yielding targets. Additionally, killing racers will still give you dark eco, which can prove to be immensely useful.
Focus particularly on green eco pick-ups for health and yellow eco pick-ups for offensive weapons, as these two will prove more useful. Your target moves quickly, so weapons that deal damage quickly as opposed to defensive weapons will be more effective. A full dark eco meter also helps quite noticeably.
Pick a sturdy, durable race car over the faster ones. Survival of the fittest comes into play here more than top speed and turbo, as opponents are more persistent in targeting you since kills are the whole point of the race, and you will be their only target until your car is destroyed. For this reason, be sure to reserve effective defensive red eco weapons (such as the shield system or attack drone) upon picking them up, and don't be afraid to waste negligible defensive weapons upon approaching another red eco pick-up to increase your chances of surviving a targeting. While speed could still be a factor, it does not compare to durability.