Tropical Apprentice BOTD should NOT be an easy badge, as it requires a lot of grinding, which most likely you cannot make through the daily if you are a newcomer.
I hope the following help:
I managed the Upward Climber using 4x Clerics (1 point healing rest dmg) and 2x Rangers (full dmg). Ofc, I was buying all possible Armory upgrades and autobuyers were all up. It just happened a little bit later when PL4 lighted up, but I did not prestige there at all.
I think the easiest way to get Millionaire BoTD is to farm 100 gems and just go ahead and buy the gold from the shop instead of stacking gold coins. In this way you can also spend on upgrades and proceed rather than farming the same level over and over.
Would you consider adding a button to make everything Auto? Instead of having to click on every upgrade after prestige, it would be helpful to just click once and buy everything.
For the BOTD you can finish the game and in the end you get a table with the total monsters killed. Maybe this can be used as a screenshot in the report missing achievement section.
You can manage to complete the game with the following setup:
Soulseeker +Atk, Entropyalien, Chakra +Atk++HP, Scarface ++Atk+Hp, Corpseking+++Hp. Make sure to use the powerful gems from the left side of the gem tree.
 "Gun Range Idle"){kind=icon}
 "armygrid"){kind=icon}
 "Tropical Merge"){kind=icon}
 "Incremental Adventures"){kind=icon}
 "Grow Defense"){kind=icon}
 "Mojo Melee: pvp auto chess"){kind=icon}
 "That Pokeyman Thing Your Grandkids Are Into"){kind=icon}
 "A knots story"){kind=icon}
 "Incremancer"){kind=icon}
 "Monster Clearer"){kind=icon}
 "A Grim Granny"){kind=icon}
 "Sticky Sorcerer"){kind=icon}
 "Pocket Creature PVP"){kind=icon}
 "Help the Hero"){kind=icon}
 "Factory Balls 2"){kind=icon}
 "Bunny Invasion: Easter Special"){kind=icon}
 "Toss the Turtle"){kind=icon}
 "SHIFT 2"){kind=icon}
 "Defend your Honor!"){kind=icon}
It is in very active daily development. Please share any ideas if you have.