Due to Islay's passive she is forced to play extremely passively. Your main priority should be to get the star lead by taking most Bonus panels you can. If Islay can get the star lead, she is extremely difficult to take down.
If Islay is far behind other players, she should consider instead prioritizing Draw panels as cards are her only way to initiate fights.
Think twice before using cards to start fights, especially costly ones such as her hyper. Sometimes, Islay is in a good enough position to win without starting any fights and spending stars on them may reduce her lead.
Cards that can force fights such as Assault and Gentleman's Battle are recommended to allow her to start fights. Ambush is usually a lesser choice however due to the cost and specific requirements to use as well as taking up deck space for battle cards that allow her to get more value out of fights.
Big Magnum and Final Battle allow Islay to more easily KO players in the few fights she'll be able to get. These especially pair well with Gentleman's Battle as fighting full HP players is unlikely to result in KO without the help of battle cards.
Sink or Swim is another good card for Islay as it combos very well with Rival to pick off low HP targets as she will still have 1 ATK to secure kills and gain an extra 25% stars.