One of the main unsolved problems is the electromagnetic shielding, both front and back (as you need to turn to decelerate). Even at 0.08c every speck of interstellar dust has enormous impact energy, far worse than the radiation of your own bombs. AFAIK this is unsolved.

follow-up: here is what wolfram alpha spits out for a 0.1 grams dust particle hitting you at 0.08c:

https://www.wolframalpha.com/input/?i=1%2F2+*+10%5E-4kg+*+(0...

it's 35% of the fission energy released by totally fissioning 1g of U-235!

i.e. I don't know whether this it's feasible to just have a heavy water & lead shield, as 0.1g is fairly optimistic to be the heaviest particle hitting you. Already at this size we're in range of tactical nuclear weapons.

You will essentially kill dozens of people once they hit an interstellar cloud with anything bigger than a sugar molecule at 2/5c.