The second battle with Augustine takes place towards the end of the game's storyline. Regardless of whether you started mission 17a, connected with good karma (Expose Augustine), or 17b connected with bad karma (Kill Augustine) the course of the battle in the atrium (the rooftop of the D.U.P. skyscraper) will be the same.
The showdown consists of two parts and the premises of its first phase are similar to the ones, during the fight with Brooke Augustine. Therefore, you should focus on maintaining a safe distance from the opponents and avoid her main attacks, which is throwing large items at Delsin.
Augustine also learned several new tricks, since the last meeting. I recommend that you, first of all, keep running around the atrium, because she is able to immobilize Delsin (the rings that appear on the ground), and also send two types of blades, against him (you can dodge to the sides from them or jump above them). At this point, it is worth adding that in the case of critical damage, it is worthwhile to return to the starting points and hide behind pillars located on the left and on the right(they will be even more helpful in the second phase).
TO deal damage to Brooke you should use the best available attack, from the Video category, i.e. Bloodthirsty Blades. The game will let you replenish your Video energy levels and you can do that by reaching the monitors at the other end of the atrium. Drain them for energy only after Augustine finishes her current attack and, it would be good if you had the upgrade, which would allow you to cut short the draining, by a half.
Just like in the case of the fight in the fifteenth mission, you need to try eliminating the objects around Augustine, thanks to which she will start to take damage and she will, finally, land on the ground. You need to run up to her, then, and press the Triangle to land strong kicks. After several repetitions, the game will allow you to launch your special attack. Press any button on the d-pad. The successful attack will result in unlocking a category of powers connected with concrete, and in ending the first phase.
Right after the second phase of the battle starts, Augustine will turn into a huge monster. Do not bother about the fact that you cannot attack her, for now. Keep running around the atrium and try avoiding the boss's attacks (ground slam and large projectiles). Once again, I remind you about the pillars near the starting point (an example in the above screenshot) because the boss will not be able to approach Delsin, if you stand behind them (it will, e.g. block on a tree). and/or will be unable to take his health points with the strong ground slams. It is worth remembering about this important facilitation, for the duration of the entire second phase.
Avoid Augustine's attacks, up to the point when there will appear Eugene and throw the first Core Relay into the atrium. Do not haste to reach it and wait for a good moment and take up energy from it, only then (by pressing the touchpad. Delsin will unlock a concrete power connected with faster and safer movement - Boulder Dash. Start using it, of course (Circle) thanks to which you will avoid taking serious damage.
Note- The Concrete power bar regenerates spontaneously so, while fighting, you do not need to search around for spots to about replenish it.
You still need to avoid Augustine so, keep running around the atrium and try to hide behind pillars. After Eugene throws the second core into the building, wait for a good moment again and take up energy from it, in order to unlock the first offensive Concrete power- Concrete Shrapnel (R2). from now on, you can attack Augustine at a distance. However, do not expect that her health points will start do dwindle quickly, because the power is quite weak.
While attacking Augustine, do not miss the moment at which there lands another core relay in the atrium. Draining it for energy will result in unlocking a defensive concrete power Concrete Thrusters (L1). It consists in performing far jumps which help you move around the arena efficiently and hover in the air, and this is what is useful, if you need to avoid the attacks under Delsin. Continue fighting by using the Concrete Shrapnel to deprive the boss, slowly, of her health points.
After several moments, Eugene will throw in the fourth (the last) core relay. Draining it for energy will unlock the most powerful concrete ability- Concrete Barrage. You activate this attack by pressing R1 and it deals the most damage so, I recommend that from now on, you keep using this one. Additionally, what speaks for this is the fact that you will not have to worry that much about Heavy Ammo because, in the case of the Concrete category, it also replenishes spontaneously (you just need to wait several seconds).
Since the moment in which you gain access to Concrete Barrage, Augustine will be using new types of attacks herself. She is able to "Flatten" herself and move all around the atrium floor, as well as turn into a kind of a snake. In both cases, it is a good idea to keep hiding behind pillars, jump, run around the atrium and use dodges, reinforced with Boulder Dash and Concrete Thrusters.
For the rest of the battle, you should be focusing only on effective use of Concrete Barrage and on avoiding the snake-boss's attacks, i.e. the big projectiles thrown towards Delsin, and snake attacks. After Augustine's health bar reaches zero, the victory will ensue.