I made myself giggle with this saying today, it means “approach a situation carefully, be cautious and patient and you will succeed”.
“Catchy” in the context of a pursuit, isn’t a word it’s just using alliteration for effect and humour (could be parodying a non native English speaker, who uses “broken” English).
“How’s your website going Craig? Any new customers?”
“Yea! It’s going well, I’m just building it up, and I have some regular students now: but it’s all going in the right direction, slowly slowly catchy monkey!”