Constant bullying may not be the best approach. 4-5 HP characters even with 0 defense can survive shots with ease and do damage back. With this in mind, ignoring players with more than 3 HP can be better. The player should focus on Encounter panels instead.
Since Star Breaker can't use stars as a win condition, try to prioritize Encounter panels early. Once a player hits their fourth norma check, the Boss panels show up, and it will substantially more difficult to get wins until the boss is defeated. Thus it may be a good idea to avoid getting to the 4th norma check until another player has.
Surviving combat against Star Breaker is very important, because unlike Encounter panels, players give two wins upon defeat. Characters with high defensive stats and cards such as Tactical Retreat and Shield will drastically reduce the chances of being KO'd. Warping with Here and There will sometimes create distance as well.