This ended up being quite long, but here's my strategy and how it worked out. I'm hoping it's clear enough. Feel free to ask if there's any questions.
My strategy begins during a shorter practice run. I figured out early on that the more lots she could get in to the better. Due to this I made sure to write down the lot values of literally every lot/house/apartment available in the game and had them sorted by value. As for apartments I wrote down the lot value both for moving in and for after having moved in during the practice run. These were a bit more of a challenge as the lot value would sometimes increase when moving in.
When creating my sim I made her a Spellcaster who was also a Kleptomaniac(she never actually swiped anything from anywhere as I didn't know if that would be considered editing a non-home lot), Freegan and Loves Outdoors. Let's say she in some ways wasn't the nicest of sims and lived off of others a lot though.
I first moved her into Oak Alcove as that was the cheapest empty lot I could find. For this and the next places she lived I added lot traits to get them out of the way. The ones I didn't add in these places were the Celebrity Home and the Vampire ones. I left the Celebrity Home for when moving in to the celebrities and kept the Vampire ones for when in Forgotten Hollow. She didn't stay on these empty lots for long, but started out making a few friends and found a few frogs to breed for money and such.
Once I got her into an apartment I created a painting club to get to know people and get a bit help making money from the people I would eventually move in to. This club I only ran fairly early on when on lots I needed to spend some time to get the lot challenges done. I also had her do a lot of painting these places as I wanted to get her somewhat famous to easier get to know the famous sims. I always brought the easels I bought with me when moving, but I left everything on the lots that had been there when moving in. In one instance I had to buy a shower on an empty off-the-grid lot, and this I brought with me before I eventually sold it as I no longer needed it.
As some apartments were a bit close in value it was crucial to move into them in the right order. In a few instances I used the gremlin lot trait to break items on purpose as this would decrease the lot value before moving out, and therefore allow for more moves when the apartment value increased after moving in. This might not have been necessary and might mean I lost a bit of value though.
Since most apartments and houses have a higher move in value than when moving out, it was technically possible to move to gradually cheaper places while it was still more expensive when looking at the move in value. Again doing them in the right order was necessary for this to be possible. This I did in one instance when the move in value of the apartment was higher than I had written down for some reason.
I mostly merged households when moving her in with others. The first one she moved in with was Salim Benali in his apartment. Him and the next few she moved in with she kept in her family to help her paint some more and earn money through any job they already had. I usually split her from household and moved her alone to the next family later on though. As she was living off of others a lot she did often take their money with her when she moved away from them. For the most part this wasn't necessary as she had a lot of money by then though. Also, one of the sims living with my sim won the lottery, but again that money wasn't something that was needed as she had enough already.
While in a few different apartments in San Myshuno I did the Cursed, Filthy, Gremlins, Grody and Spooky lot challenges. The Reduce and Recycle I did where it was already on the lot in Evergreen Harbor. Off-the-Grid was done at least on the lot that has this trait in Sulani. I always checked every lot for lot challenges already there to make sure I didn't miss any as well and did them again if present.
I was struggling a bit with the lot challenge Creepy Crawlies as it never gave a happy moodlet after encounters with the bugs. This lot challenge I waited with until my sim was living in one of the somewhat cheap houses. After trying for a couple of days, I decided to travel to Selvadorada for some hours to buy supplies as I couldn't seem to beat it any other way. Shortly after this happy moodlet showed up and she could move on.
When I got to the houses with sims living in them, I made sure to befriend the ones she hadn't already made friends with. Eventually some new sims moved into more houses and there were more sims to befriend so she went to visit all of them.
In StrangerVille I think one sim I was to move in with died before I got that far. The lot value decreased by a lot after this. As she by then knew enough spells she used that to break items and even set fire to a few of them to decrease the lot value enough before moving out to move in to where that sim used to live.
I ran into a few bugs throughout the play, but found ways to work around them. The first two of these were the one with missing apartment doors and spellcaster points not being given when leveling up. Apartment doors missing certainly made it harder getting to befriend the sim living there to move in with him as I couldn't knock on the door. Due to this I had her mostly working on her spellcasting in the hallway outside his apartment for almost two days with only going home during the night. Eventually he came out of his apartment and she made sure to become friends with him. The last bug or something I ran into was when the game froze for I think almost an hour in real time closer to the end of the challenge. Luckily it unfroze after all this time, but it was running without me being aware of it for a bit then.
She ended the challenge with Judith Ward in her house. In total she lived in 130 places, had 43 lot traits and did 8 lot challenges. The lot challenges I didn't do were Simple Living and Wild Foxes as I don't yet have the Cottage Living pack. I think I have all the other packs with worlds in them though.
