How do I beat the Picus boss?

Note that Eliza will always warn you before the boss uncloaks to charge you in melee. Try to position yourself around one of the large power cells around the room. When the boss uncloaks to charge you, place yourself between her and the cell, and she'll charge the cell, take damage, and be temporarily disabled (I've found that the easiest way on the hardest difficulty to do this is to jump over her as she charges, but I'm not sure if this is possible without the cybernetic leg prosthesis). Feel free to squeeze off a few head-shots with your weapon of choice while she's incapacitated if you have the electricity-shield upgrade on your dermal armor;otherwise, jump like a bunny on crack if the electricity damages you to avoid taking the full amount of damage. To my knowledge, there is no immediate "safe" place to hide from the electricity damage, but I could be wrong here.

If she still has some health left after charging all four cells, a fairly easy way to get some decent damage in is to stun her with your stun gun or EMP grenades and shoot her a few times with your weapon of choice. Then run. Run like demon monkeys are after you and hide like a scared NPC.

You can also "see" her while she's cloaked if you have the smart vision augmentation; this comes in handy to either plan surprise attacks or get to a safer location, as the boss moves quite slowly while cloaked, even on the hardest difficulty.

It took me about 20 stun gun shots to kill this boss on a non-lethal playthrough.

You haven't mentioned what you have in your inventory or what augments you have chosen.

You should try and listen to her footsteps when she is cloaked. You can easily tell the direction she is approaching from. As soon as she uncloaks, move away from her and try shooting her at the same time. I also read somewhere that you can watch the wet floor for footsteps to find out where she is. Personally, I didn't find this to be of much use.

She usually stops after that initial charge and launches an attack with her augments. If you have an EMP grenade you can disable her for a few seconds and empty your arsenal at her. If you have some kind of fast firing weapon like the heavy rifle or combat rifle or machine pistol, it really helps. You can also move in closer and launch your Typhoon Augment(if you have it) after the EMP.

If you don't have any lethal weapons on you, you can look in the lockers to the sides of the circular room. You will find some weapons and ammo. This is easier if you have cloak augment.

When she is charges and fires at you at the same time just hide, and use your hypostims or painkillers. I think you can find some in the same lockers I mentioned above.

And a bit of advice for the future bosses in the game: even if you are going for the pacifist play-through for the rest of the game, keep lethal weapons in your inventory for the boss fights at least. And EMP and Gas grenades really help in slowing them down.