This wonder is very difficult to build in a standard game since animals only spawn up to a certain point. However, there are a few things you could do to get that trophy. The game option Wildlands doubles the amount of animals that spawn. It's dangerous for early settlers but a must if you want to get the Menagerie. You will want to research Animal Husbandry very quickly so that your Recon Units can get the Subdue Animal promotion, then go quickly further up the Recon line to build stronger troops. Meanwhile, build lots of Scouts and level them up with Goblins, if possible, change to Apprenticeship to get those extra 2 xp. A civilization with a strong synergy for the Recon line would be useful here, for example Ljosalfar or even better Svartalfar who get +1 attack strength for Recon units.