In the interest of keeping it civil and answering the OP's question, in the approximate order of difficulty:
Fitment-
The first issue will be if there is enough room between the radiator support and the firewall. With a transverse mounted v6, I wouldn't bet on it working. Based on a quick Google search, the 3.5 out of the Impala is a 60 degree v6, so fairly wide (or deep, whichever way you want to look at it). With or without the battery, this will be hard to make fit... either the core support will have to be re-engineered or the firewall will have to be modified. Consider that you'll probably also need a custom radiator and fans of some sort.
Mounts-
Assuming the engine can physically fit within the confines of the engine bay, the next issue is mounts. This is actually somewhat straight forward as it's just a matter or hanging the engine in place. At its simplest you could probably get somebody to weld you some form of adapters to the chassis to accommodate the stock v6 engine mounts, assuming they are in remotely the same location. More than likely a new mounting system would have to be engineered with either whole new mounting points for the engine or some kind of custom CNC mount.
Transmission-
Assuming you get the thing in there and hung in place, next you have to get power to the wheels. Again at a minimum you would need a custom axle. Places like driveshaft shop could make them. When you have your mounts designed you have to make sure the output of the transmission is somewhat in line with the front wheels or you're just asking for problems in the form of wear and breakage.
Wiring-
Surprisingly, this may be one of the easiest parts... which is not to say it's easy. You would either lift the whole v6 harness and graft it in to your cars body harness, try to get the 1.4/1.8 harness to run the v6, or get a custom harness built. Regardless, the chances of the car ever passing an inspection again are becoming less and less.
Exhaust/Intake/Fueling-
This is definitely the easiest part, but everything will have to be custom. Probably a custom line from the Sonic's hard fuel feed, then a custom intake, and exhaust from the manifold's back... assuming you could keep the manifolds at all and didn't have to make custom headers for fitment.
1.4T Turbo-
I am going to extremely over-simplify this, but feel free to ask and I'll elaborate further. A turbo is rated for a max horsepower (Garret, Precision, Turbonetics, etc all do it this way) because oxygen + fuel = horsepower. If a turbo flows the most air (and therefore oxygen) possible, then it doesn't matter if it's on a 1 liter engine or an 8 liter, it's only going to be capable of a certain amount of power. Maximum wheel horsepower we've seen on a stock turbo is right at 200whp, as far as I recall seeing, but let's say 220whp to be generous. The 3.5 V6 is close to 200hp stock... the turbo probably can't physically flow enough to increase that number an appreciable amount. Add on to that the fact that you have to get 3.5 liters of exhaust through the tiny exhaust turbine on the stock turbo, and you'd probably lose power.
Another fun little math equation: 14.7psi = 1 atmosphere (approximately). If you boost the 1.4t to 14.7psig (29.4psia) then it is roughly the same as a 2.8 liter engine with no turbo (again, this is very approximate). 3.5 / 1.4 = 2.5 and 2.5 * 14.7psia = 36.8 psia or 22.1 psig. Basically, the turbo would have to crank out 22 psi on the stock engine to equal the flow requirements of 3.5L NA. Again, putting the stock 1.4 turbo on the 3.5 would gain very little, if not lose power.
So now, how will this swap cost 2 to 3 grand tops? I'd be shocked if it could be done for that in parts alone. I'd see more like $5000 in parts plus 200-300 hours by a master fabricator. If you're a master fabricator then go ahead. If you're not a master fabricator then assume you're going to pay someone else close to $100 per hour for labor.
I really should just make one response like this for rwd, awd, and fwd swaps and just copy/paste it to every thread like this that gets posted.