So the layout of boxes is going to be: switch A -- Light 1 -- Light 2 -- Light 3 -- Light 4 -- switch B? And you only want to pull wires between neighboring boxes, and the Light 1 box has constant power?
Then the diagram is almost correct, it doesn't comply with the somewhat recent requirement that a neutral conductor be provided at one of the two switch boxes. [You won't actually need the neutral conductor for standard 3-way switches, so you just leave the end capped in that switch box.] So you'll need to have 4 conductors between adjacent boxes, except Light 4 -- switch B can be only 3 conductors.
Using 12/4 or 14/4 NM cable would be nice, with black, white, red, and blue, but it's more than twice as expensive as /2 NM cable. So the diagram shows the use of a pair of /2 cables to get 4 conductors. If you do that, it's best practice to run those two cables on top of each other, so they follow exactly the same path. And one cable should have both of the conductors reidentified to 2 new colors, e.g. blue and red; those are the travelers between switches. [The black dot on some of the white wires in the diagram represents reidentifying them. Reidentifying the black traveler isn't strictly necessary.]
BTW, Light 1 box is going to have 10 conductors entering it, so it will need to be 22 in^3 if using #14 NM, and 24.75 in^3 if using #12 NM. The other ceiling boxes will only need to be 18 or 20.25 in^3. If the lighting fixtures use a canopy with a volume labeled on it, you can add that volume to what the label on your ceiling boxes says.
Cheers, Wayne