What I've been doing and has been helping is start typing the name of the item into Etsy's search, and see what suggestions come up. Like if it's a Cheetah photograph, I start typing cheetah, and it gives me a small list of cheetah related searches that people have recently done. Then I'll try the same thing for "wild animal" "art" etc. Obviously only use the ones that are relevant, but you might be surprised at the different variations people are looking for.
Also look at your previous month's search result stats, see how people are finding you, and make sure those tags are in your items.