This boss can be an annoying pest to fight.
He has 3 phases that get progressively more complex. You also win a heart after every phase and when you defeat his copies in the 3rd phase
For phase 1 he uses 2 or 3 laser pulses, several second laser eyes and rearranging the fighting area. The pulses spawn the slowest of the entire battle. At the end of the phase (You can tell when it's the end as he always brings the 9 blocks back into a square and then change it again) he spawns 3 ghosts and after those he becomes small and you have to jump on his head 3 times to.
For phase 2, he uses 2-6 laser pulses which spawn faster and variable length laser eyes (You will likely have to triple jump). Unlike in the first phase, there is no pause between those moves so expect to have to dodge a laser pulse immediately after he is done with laser eyes. Also he will rotate the field while doing laser pulses and the pulses don't move with the field (You can rotate into them). At the end of the phase, he spawns 6 ghosts and after you defeat those he appears. This time he will send out a pulse after you hit him in the head the first 2 times.
Phase 3. This phase starts with a laser pulse barrage faster than anything in phase 2. The second part he adds elevation like he did when he summons ghosts and you have to dodge his laser eyes while platforming. He returns everything flat, summons ghosts and then starts doing laser pulses and laser eyes while you have to defeat the ghosts. Once you defeat the ghosts he spawns again and this time when you jump on his head he also spawns a clone.
Beat him and grab your book and this achievement will pop. If you stay and watch the credits, you can get a second.