This enemy (Department of Unified Defense Agent) is encountered during the eighth main mission (The Test), that is when you are trying to cross the bridge between the north and south part of Seattle.
A duel with the agent takes place on a large arena located near the southern part of the city. Let us traditionally start with a few words about the boss's attacks, which is because they are quite diversified and they inflict considerable damage, so you really need to make effort to avoid them. One of the main attacks that the elite D.U.P. agent has, is casting massive cement blocks at the main hero, which you can avoid by running or taking appropriately big covers.
Another major attack the boss has is firing auto-targeting missiles that move under the ground and inflict damage upon contact with the main hero. In this case, it is highly advisable to often perform dodges and run around all the time, hoping that an enemy missile will miss Delsin. Otherwise, the main hero may be seriously injured and temporarily dazed, thus getting exposed for further attacks from the boss.
The last attack D.U.P. agent has, is used in the later phase of the duel. The distinguishing feature of it, is that the boss temporarily ceases fighting at a distance. Namely, he will try to perform a single melee attack. As with the previously described auto-targeting missiles, the key to keeping Delsin alive is to avoid such charges by dodging and running, as they may inflict serious injuries.
So much for the boss's abilities, now some information on how to deal with him. The first thing you need to do is to switch Smoke power to Neon power by absorbing energy from one of the neon lights in the area. But do not rush into this (that also applies to regenerating the energy bar later in the fight), but first make sure that the boss is not currently in a position from where he could easily interrupt the charging process and weaken Delsin at the same time. By the way, I recommend getting the improvement that shortens energy absorption time, although you can handle even without that.
Theoretically, you can attack the boss with all available ranged attacks (do not try to get near it - melee combat is not an option), but the best result comes from using a combination of Laser Insight with Phosphor Beam. Start by holding L2 button and right after that hold R1 (Phosphor Beam attack needs a moment to charge up). Now try to aim directly at the boss while in slow motion mode (as in the picture above), waiting for the moment when the missile launches.
Using Phosphor Beam power will only prove successful and take away a lot of hit points from the boss, if the energy beam hits directly at him and not at the concrete elements floating around. From now on, keep repeating all the steps as described above and be sure to frequently regenerate power by absorbing energy from neon lamps, because Phosphor Beam attack requires Heavy Ammo. Reducing the D.U.P. agent's health bar to zero will terminate the duel.