You can do any tower by buzzer as in my video here https://www.youtube.com/watch?v=8x0q-Zxb-OQ Scope out the tower to find a part of the top platform which has no wooden fence. Get as close to the tower as you can without touching the projecting roofs. Press Ascend and keep it pressed then jam it forward when you reach the platform then "E"! Even if the buzzer crashes you should still be OK.
I have played the game several times and eventually managed to make the jump. It might sound silly but it helps if I tense my body up as though I was really going to jump.
OK, that tower is a bit of a pain.
You can always get there with the buzzer by hovering just below the max allowed height, quickly rising to the lat platform height and hitting forward at just the right time. But, the regular (climbing) way also works.
At one floor, you have to shoot some boxes to gain access to where you need to jump to a "climb rope". Once those boxes are out of your way you have to duck down to fit in the opening, then stand up as soon as you can to give yourself the max running room. Run, jump, and climb. Then you walk a ramp to get to another climbing rope, climb to the next floor.
Now walk around till you see almost a repeat of the lower floor, you have to run and jump this much larger gap to reach a "climbing rope". I got it to work ONCE out of many tries. What works almost every time is to walk further around the floor so the climbing rope is visible through a broken section of the wall. It might not seem like you can make it jumping at the 45 degree or so angle, but I've done it maybe 8 of 10 tries, so it's not that bad. Just make sure you as far back in the broken section as possible, then run/jump in one motion to reach the rope.
The rest of it is standard easy stuff.
Good luck, give it a few tries, I have confidence you will nail it.