I reached out to the devs for help after having issues with several achievements.
"For the up close and personal achievement, you have to complete the game using only melee weapons. But some towers require using a sling or arrows to shoot gongs and open the tower so it can be activated. I believe this was also a change with the Loathing update and it seems like using a ranged weapon will void the melee only achievement. Can you clarify?"
Again, in these cases, the weapon interacts instead of causing damage, so activating gongs with a ranged weapon will not void the achievement.
I still couldn't get the achievement to unlock. The dev offered more info:
Currently it seems that unexpectedly, jelly fish being killed counts as the player killing, which is not intended, and has been fixed locally. This impacts up Back to basics, Up close and personal, Keep your distance, as you have correctly identified. To work around this, for now, I would advise you avoid killing/interacting with/hitting jellyfish.
I finally got this achievement to pop in a run where none of the towers required shooting elevated gongs, which is pure RNG for tower progression generation. I also avoided all jellyfish in the boat. I cannot verify that shooting gongs with a ranged weapon is allowed since I didn't need to.