A Hat in Time

If you want to do this the cheap way, there's a community workshop mod that gives you a badge that enables invulnerability. You pretty much can't lose health when this badge is on; one of the only exceptions I noticed is if you let the giant bomb in the Snatcher boss fight explode. Download it here if you're so inclined: Aura Badge

If you're doing this in the cheap way, also enable assist mode in game settings to make the bonuses in each death wish level unlock automatically when completing the main goal. The only thing this doesn't work for is candles (which are all extremely easy anyways) and the 3 community rift death wishes (which are also very easy to do). Just disable assist mode when doing the community rift death wishes or else you bar yourself off from getting the required bonuses in those.

Finally, one of the death wishes is for completing 40 tasks (30 if you use assist mode) in a modified version of the "Ship Shape" act from Arctic Cruise. You can use the InfStop workshop mod to trivialize this task. This will grant you a modified version of the time stop hat that has no cooldown or time limit to its usage.

This should still take some hours to complete with these cheeses in mind but its much much easier to get 111/111 stamps this way. If all you care about is getting the achievement, and not being cool by doing it legitimately, this is a totally valid option.

Chapter 6, Act 2 is where you get this. This achievement involves a lot of good RNG, memorization, and patience. If you don't have that, there is a way to cheese this using an infinite stop hat mod.

Download from the workshop here: https://steamcommunity.com/sharedfiles/filedetails/?id=1990767736

Yes, it is much less cool to do it this way. But you can if you'd rather save yourself the trouble.

Activate the InfStop hat, then collect the objective, throw it to its dropoff, disable its ability for a second so the dropoff can actually work successfully, then rinse and repeat until you have all 18 tasks done. This significantly slows down the captain's meter. Just make sure it doesn't reach two full bars; this shouldn't be a problem at all. I got it first try using this cheese with no practice.

I had a ton of trouble getting this achievement. Challenge Road can be found in the mail room by talking to the mafia man, and involves completing 5 community levels in one sitting with only three lives. If you die three times, you have to start all over, and this can be infuriating when levels take a long time to complete. Luckily, there is some cheese to this one that makes it nearly effortless!

In Settings > Game Settings > Accessibility there is "Assist Mode" which can be activated. If you have a lot of trouble with this achievement and even death wishes, this will save you from it. Instead of four hearts, you now get eight. If you stand still for a few seconds, you can regenerate lost health. This essentially makes Challenge Road, regardless of when you do it or how hard it is, impossible to fail. Some months you'll get lucky and have ones that revolve almost solely around platforming; this makes it much easier compared to having other hazards involved because if you fall off you can just stand still for a few seconds and eliminate the consequence of losing a heart entirely. However, it still, regardless of when you do it, should be a million times easier with Assist Mode activated.

The aura badge, which grants nearly total invincibility, also can be very helpful here.

I know this is a bit cheap, but it's a perfectly legal method, so if you have trouble with the game, use it at your discretion.