The Good Life

There is one way of knocking this achievement out of the way and money free early on in the game and it's just as you learn how to change into a dog. You'll be tasked with finding Elizabeth using your sniffer sense and eventually come to a part with a badger blocking the path and are forced to fight it.. It is pretty much a losing battle right off the bat and the first death will give you items to use to beat the badger.. However, if you ignore using those items and continually attack the badger and die over and over again, this will +1% to each of the 100 deaths you need in the counter. These deaths do not cost money and you are forced to win the fight to actually pass the quest.

Method 2 Route A : While on the quest to carry out barrels of "vampires blood" you'll notice 2 multi-coloured barriers on either side of the room, simply walk into these barriers a few times until 0HP and you'll "pass out" and the segment will reset and grant +1% to each faint money/time free.. Do this before you carry any barrels otherwise it will reset any barrel you have carried thus far.

Method 3 Route B : As per MegaRae When you see the glowing footprints in the mine (after dynamite/computer), follow them until you get to the electric fence. Run into it a few times. You'll die and be put back to the beginning of the footprints. No money/time lost.

Method 4 Route C : As per DenverMax While in the Kingsglave searching for the hidden path, you can find a few badgers off path who will attack and kill you for a free death @ no cost to time or money, not as fast as the above but quicker than post game.

Method 5 Side Quest 'The Human Race’s Oldest Computer' As per MegaRae, where the camera shop guy John Berryman asks you to hack the old computer. You will have to answer 3 questions the computer gives you and if you get any wrong you die and get to try again. No money lost.
ETA correct answers: Lugh, Alfred, Wicker Man

The ONLY other quick way I've found (outside of quests) so far that does do +1% each death is to deposit all your money, then as a cat go get killed by a sheep (behind your house works fast) then let the vet heal you.. He'll say he took funds from you but he can't because you have 0.00 on your person and it doesn't subtract from the bank. However! this will cause time to proceed and doing it like this will gain you 100days, so in reality it works towards the 1yr achievement but also causes your photo's in the PC to be worthless for that time. Unless you just go snapping a bunch of crappy ones and upload them for minimal likes/money. It could be best to save this for post game cleanup while also working towards 1yr spent in the town achievement. You cannot reload this method, and must either finish all 100 in one sitting and then reload just to get the time wasted back or save periodically and deal with the +100 days of time.

*As Sculli suggests you can also make use of the badger slightly behind the "witches" house, it spawns near a marking spot as well as where a side quest dig spot is. Die, rinse, repeat. Just keep your wallet at 0.00 so you don't lose money.

This should give us a good amount of "how to's and where" for people looking to speed up the deaths, like always you can leave comments with more if you find them. :)