For badge, you have to unlock the ability to run all 3 research upgrades at the same time with the blue gems, not just unlocking the 3 researches, badge description is wrong.
Very bad game, if it gets BOTD again, remember to change your system time, as it works for poor mobile ports like this tricking it. Also remember to rate all bad mobile ports like this that just want you to microtransact to progress as low as you can. Would rate 0/5 stars if possible.
 "Grow Defense"){kind=icon}
 "Tropical Merge"){kind=icon}
 "Chaos Faction 2"){kind=icon}