Update: I realised you can ask Lin Lin and Sammy for help to get an extra +40% on the skill checks, so turns out no, you don't have to grind! At least for rescuing Cassie. Still no clue about the Abomination. I've tried going back to the base and defeating the core, but it won't let me near, so I assume that's not the way either.
Abomination's a challenging battle, but it's doable. There is better food in the game than stamina drinks (e.g. Your Milk then Angel Milk, or just Fish Soup (Good!)), make sure you have good weapons equipped, get the usual set of stat buffs from town, and be sure to Guard for the big attack rather than outhealing. I was able to beat it (18 str, 11 res post-buffs) without using any healing items and with really bad strategy, so if you have a few you should be able to do it when weaker than that.