Defeat the same opponent player 5 times in battles in one single game.
This achievement is tough even with a strong attacker like Yuki or Tomomo, mostly because the time it takes to first defeat the opponent, then for them to revive, then to catch up to them again, can occupy most of the match, wherein you're also potentially being attacked by other players and spending time in revive yourself. In light of the above, helpful cards are always Dash!, Extend, and Forced Revival, along with your standard battle deck. It's advisable to play on a smaller map, like Practice Field, to increase frequency of encounters with your target, but more than anything this achievement just takes persistence.
This achievement is also very doable on Kai's first scenario featuring Marie Poppo and two enemy-character players, especially on Casual difficulty. Simply continue to target the two enemy-characters, as they have the lowest hp, and occasionally Poppo to prevent her from accumulating too many stars. The same cards mentioned above are just as valuable here.
As an aside, since the achievement description explicitly states "during battles", kills obtained from Marc's X16 Big Rocket do not count towards this achievement.