How to solder a breakout board to a prototype board without edge castellation?
Here's my suggestion:


As needed, add a sufficient layer of electrical insulation between the bottom of the DRV2605L board assembly and the top of the prototype board.
With your pin header assembly, push the plastic insulator all the way down to the far end of the pins without actually removing the insulator from the pins.
Position the DRV2605L board onto the prototype board as desired.
Insert the pin header from the bottom of the prototype board up through the 0.1" O.C. plated-through holes (VIN, GND, SCL, etc.) on the DRV2605L board.  Ensure the pin header's plastic insulator is on the bottom of the prototype board, and the exposed ends of the header's pins protrude out the top of the DRV2605L board.
(NB: Use a piece of electrical tape to keep the pin header's plastic insulator pressed against the bottom of the prototype board during soldering.)
Lay this assembly flat on the workbench with the prototype board on the bottom and the DRV2605L board on top.
From the top side of the DRV2605L board, flux the header pins and plated through holes in the PCB, and then solder each pin to the DRV2605L board and to prototype board.  When soldering, 


ensure the soldering pencil's tip touches primarily the header pin, and touches secondarily the PCB pad at the top of the plated-through hole on the DRV2605L board, and 
touch the solder wire to the header pin&mdash;NOT to the soldering pencil's tip&mdash;during the soldering process.
(NB: The header pin must become very hot as it must be the means of heat transfer down into the plated through hole in the prototype board.)

After all the pins are soldered and are cooled down, remove the electrical tape that held the plastic insulator to the prototype board, and then pry off and remove the plastic insulator from the now soldered header pins.
Inspect each solder joint on the top and bottom, and rework any joints that are unsatisfactory.
Remove the flux residue from the assembly.
Using a flush cutter tool (a.k.a., wire cutters, diagonal pliers, nippers, etc.), trim off the header pins to the desired height above the surfaces of the two boards.
(NB: I recommend that you leave a stub height of about 1&nbsp;mm&nbsp;&ndash;&nbsp;2&nbsp;mm after cutting each pin. A stub is required if you later need to desolder these pins with a vacuum desoldering rework station.)