Take a look a the actual Breakthrough Starshot website
http://breakthroughinitiatives.org/Challenges/3 to get an understanding of the team's assessment of the challenges, including:
. Building a 100 giga-watt laser array (and designing a sail which can cop a blast from a 100 giga-watt laser array!)
. Gram-scale chip(s) for the laser comms, processors, cameras, nuclear power source, etc
. Pointing the (gram-scale) cameras for a planetary fly-by at 0.2 c
. Using the sail as a "Fresnel lens" for comms back to Earth
. Building a kilometre-scale receiving array to pick up the very weak signal from the spacecraft