10^35 neutrinos sounds to be in the ballpark, and if we assume solar neutrinos with arround 1MeV of energy, a beam energy of arround 1.6x10^22 J, or 16 zettaJ. The neutrinos will be at near c, since they're close to massless. I'll take as given that beam generation is 100% efficient, so we don't have to deal with wast heat. Even a slight inefficiency is going to give us serious trouble.
So you've just fired a 180 tonne, lightspeed bullet at your enemy. Recoil is gonna be a bitch.
Lets say you can't quite do 16 ZJ (zettajoule) pulses, but you can do a 3 TW portable neutrino beamer. Irradiation only works out to about 0.3 microsieverts/sec I think, which the target probably won't notice in the heat of the moment. Average annual background dose at sea level is about 3 millisieverts, with a fatal dose being about 3-5 sieverts. You'll need to hold him still for a million seconds for a fatal dose to accumulate, about 12 days.
I can suggest a better way: find a one tonne rock, put it in a sling. Use your portable beam generator to lift the rock - a 3 TW photon rocket will suspend 1 tonne in a 1g gravity field. You can fire straight through the rock, these are neutrinos after all, not photons. That way stability while you hover the rock won't be an issue. The rock will get a little warmer at about 300 microwatts/kg. Just hover this over your target and drop it on him.
To an unlettered barbarian, it'll look like you have a reactionless drive. Of course, if you know what it is, you wouldn't want to stand under it. It would be like standing under an old style xray machine. A lead apron won't help though.
If the beam has a bit of divergence, like a regular rocket or even a torch, then it should cover a good many square kilometers when it emerges from the other side of the planet, it should be well below background radiation levels then.
Much nicer drive than a photon rocket, or even a regular chemical rocket.
If you've got a vacuum certified mobile home and can do 30 TW, then 100 kg of neutrino reaction mass will get you to mars in about 85 hours. That's straight line 1g all the way. You'll need another 100kg to get home again.
If you're considering neutrinos for reaction mass for a drive system of some kind, a few more useful facts:
Neutrino interaction cross section with nucleons goes up quadratically with neutrino energy.
If the neutrino energy is above a reaction specific threshold, it can cause nuclear transmutation. For example, a Cl37 to Ar37 neutrino mediated transmutation requires energy above 0.814MeV. This was used in the Homestake mine neutrino detector.
Interaction cross section with electrons goes up linearly with neutrino energy.
So use low energy neutrinos. Radiation damage to the environment for 3 TW of 1keV neutrinos would be about 1000 times less than for 1MeV neutrinos. Neutrinos are so close to massless that it won't impact drive efficiency much at all, they will still be moving at lightspeed for all intents and purposes.