TL;DR - Island Map, C-375 with Log Carrier and Medium Log Cart. 2 trips to each mill, one or two trips to fuel station. Be careful and slow in fords and boggy sections - use manual Low gears. Do North East Lumber Mill first. ONLY USE ONE VEHICLE from the very start!
(Note - if you are familiar with the Island map, this is a great way to also get 'Blind Navigation' - Finish a level without getting any watch points, AND 'Forester' - finish a level without using the navigation map. To familiarise yourself, just start the Island map with the A-469 Jeep, and find the two Log stations and two lumber mills, and the fuel point in the south east. When you are happy you know it, restart the level. Make sure you stick to the roads and tracks directly between the Log Stations and Lumber mills etc. to avoid accidentally triggering a watch point. Also, never press select to open the map AT ALL - make sure before you start the level, that you select the vehicle you want to use as the MIDDLE vehicle out of the three you are allowed, then you won't need to switch, as you default into the middle vehicle.)
For this achievement (My Only Love), You just need to fill all the lumber mills on one map - I used Island as the Lumber mills are easy to find - using (i.e. only starting and driving) just ONE vehicle in total. I did it with the C-375 with the log carrier and medium log cart, so I only had to do 2 trips per mill (2 x 4pts per load = 8 pts per lumber mill), with an easy to manage load (easier than a carriage and trailer, and easier than long log cart).
However, any truck that can take the log carrier and medium log cart is good. You could also use a really beefy truck like the D-535 and take a small log carriage and small log trailer, if you don't mind using the trailer. You can easily get by with the C-375 though, if you use manual gears and low 1 or low 2 for very boggy / muddy sections, and Low 3 and Low + on good sections. I did have a bit of trouble with the big ford on the way to the North East Lumber Mill, but if you stick to the Northern side of the ford, there are trees you can use to winch.
Other than finding your way around (which is pretty easy on Island), the only other issue is fuel management, but the C-375 is at least quite easy on fuel, despite a relatively small 270L tank. I did the first two loads from the Northern log station to the northern lumber mill, then it was a bit low on fuel, but it was enough to get down to the fuel station in the South East. If you run out of fuel, you are stuck, because you can't switch to another vehicle to fill it up, so keep an eye on it, and if in doubt - fill up first. The whole session takes less than an hour anyway, so an extra fuel trip is doable, though shouldn't be needed if you go straight to the first two loads at the nearer Log Station / Lumber Mill.
The technique I used was selecting the truck I wanted to use (C-375) at the very start of the game, as the MIDDLE one of the three vehicles you can choose. This makes you spawn into it by default, while the engine was off, still parked at the spawn garage. I set it up with the log carrier and medium log cart, and included a spare wheel in case I got a bit of damage. I then went straight and left, past the first lumber mill, left at the junction on the concrete road, down over the big ford, over the little ford, and along and down the hill to the North East log station. Load up, and head back the exact same way to the Lumber Mill near the start.
Do this twice, then you will be low-ish on fuel, so head straight down the main road in the middle of the map, through the block post and down to the fuel station in the South East. Fill up, which will be enough to finish the mission in the C-375. Head left to the 2nd garage, and past it to the log station just to the north (go via the road to the left, and head round to the right, if you don't want to get stuck in the trees. Remember you can't switch to another vehicle to winch you out). Load up, and head West, across the big track (this bit is very boggy up a steep hill and across a bad road - be patient and use Low 2 or 1),
Go through the forest on a little track, over and across the main road you came down earlier (DON'T check the map if you want the 'Forester' achievement!), and down a little track to a ford, heading South West, and just follow the track - it gets a bit vague over some sandy bits, but if you've familiarised yourself with it, you should be fine. follow that track all the way to the South West Lumber Mill, unload, and repeat (no need to fuel up again, you'll have enough in the C-375. As soon as you have put 8pts into both Lumber Mills, the achievement will pop. If you haven't unlocked any watch points, you will also get 'Blind Navigation', and if you haven't opened the map, you will also get 'Forester'. Enjoy! :)