The trophies you cna score are rated in Bronze, Silver, Gold, and Diamond. Its linked to the scoring value of the animal itself, I think, as long as you hunt it ethically and thus do not ruin the scoring. The high-value animals are usually not the ones moving in first, they are rare, may be "protected" by a screen of low value "guards"(like carriers surrounded by a screen of escorts
), or may immediately spook if you use a caller, or move in on them instead of letting them come to you. They are more difficult to hunt.
I did not find Gold and Diamond ones before my skills were seriously scaled up, maybe becasaue some oif these skills could be interpreted as a "sharpening of senses". But that is my interpretation only.