We're going to spam multiple achievements all at once here.
It will add progress towards these as well, but you don't need to do all the extra stuff for these.
Select your plane. I used the Extra 330LT because it flies low and slowish. Rain isn't constantly falling so you want one that won't fly through it too quick when it does rain, and if you get to high you will see less rain.
Select a departure and an arrival airport that are far apart. I used EIDL Donegal in Ireland to KJFK Kennedy Int'l in New York USA. It's almost completely over water so their are no unexpected obstructions to fly into. Now under the airplane thumbnail you can change from VFR, to IFR (Low-altitude airways). (VFR stands for Visual Flight Rules, IFR stands for Instrument Flight Rules. The more you know...)
Set Flight conditions to Rain, and time to night. You will have to periodically adjust the time so it stays night during the flight.
You may want to save the setup at this point so you can easily get back to it.
Now you can go to the runway and get ready to fly.
Go to Assistance and Airplane Systems then turn Unlimited Fuel on.
As soon as you are on the runway, pull up the weather window and select the lowest cloud level. Raise the slider for "Altitude (Top)" up to 20,000 or so, this will keep you from flying above the rain level. Now slide the Coverage slider to 100 so there are no clear areas for you fly through. It won't rain all the time, but it will rain a lot. There is an upper limit for getting rain, but I rarely went above it using this method.
NOTE: If you are flying out of far northern airports (like Canada), you may need to manually raise the temperature in the Weather panel or your plane will ice up and crash. On the Weather Settings look for the 'Temparature MSL' slider and increase it to around 25 or higher.
Close the Weather window and pull up the AI Control window. Turn all 3 of these on and go do something while the AI does the work.
User KawiNinjaRider7 commented on the solution for IFR that progress is only saved when you land for that achievement. I had an issue where I lost hours of progress for all time based achievements when the game crashed after 8 hours of flying. So to be safe, land or exit to main menu periodically to keep from losing progress.