If you are going for Proving Grounds points, prepare to invest into long battles, where the skills, summons, and maybe charges are accounted for. This will take some time.
If you are going for badges, then I can help you with a few suggestions. Beating the first stage quickly and easily is the goal here. After, you can evacuate from the battle altogether to collect easy, yet mealsy gains. There are several methods to execute this repetitive excercise. Exploiting elemental weakness rules is essential, you get penalized for not doing so. Your allies should at least be in the fire element, particularly good ones. In this period, exploit the aura of your support summon. An increase in attack percentage is what you are looking for. You might want to invest in a wave attack if optional (thru class or character, but I hadn't seen a weapon [charge/skill] nor summon [call/aura] capable of wave attacks just yet). If unable, attack rate multipler would help. Not sure about bounty debuffs due to badges being in wooden chests.
Why do this? That "Feb 2019 Proving Grounds SSR Ticket" can help with getting something good. It might be related to the correlated draw event period. I just missed out on the character draw period, but summons are much rarer. Got "Sylph, the Flutterspirit of Purity".