MisterDoctor

no refueling, though that would have been the next plan if this didn't work out. (also not single-stage.) the trick I used was to make a very small probe with no re-entry capability, and then I could max out the dV more easily. as long as I could get anything to just touchdown and get back to Tylo orbit, then at least I could "rescue" the probe and that would count. so, I did not make a ship that by itself was capable of the return trip; it could get back to orbit of Tylo (with 1600 dV left) and that was it. it also did not contain a kerbal. to complete "plant a flag on tylo" I stranded a kerbal there separately. (this is the first time I've made it this far.) (I don't use any mods, though one thing I did was add my own part which is an FL-A10 adapter fuel tank (a 0.625m to 1.25m fuel tank adapter), which is a noticeably absent part IMO. I think there was one in this rocket above the 1.25m reaction wheel.) Only got a couple screenshots and nothing from Tylo: My separately stranded Kerbal:

Yesterday I completed "Return to Kerbin from the surface of Tylo" which I had felt was almost impossible to accomplish. I finally did it with a 17500m/s dV rocket that also had good TWR on the right stages. This only was able to get a probe to land and return to orbit with about 1600 dV left (but no means of re-entry). I then sent another mission to Jool to bring the probe back to Kerbin orbit, and then a third mission to grab the probe and safely re-enter and land it. (Since I'm playing without reverts, I used a Sandbox save to design and test this rocket. The first test did not have enough dV. The second test did not have enough TWR. The third test found a happy-medium and managed to get back to orbit. I then loaded the rocket into my main save and did it for real.) Today I "landed" on Laythe for the first time, meaning that I deorbited a satellite to get "landed on" to complete. I think I could have landed softer but took too long of a break between burns and ended up landing hard. Almost every part of the satellite was destroyed save for the CPU itself (and one broken solar panel attached to it). It rolled gently downhill for a good 15 minutes before I could return to the space center. Next I will hopefully be splashing down and "walking on" Laythe for the first time. (Been playing ~5 years, have 2500+ hours, and this is the furthest I've gotten into the game before.)