Time Out says
The best time to visit Kusu is in October, the ninth lunar month. That’s when pilgrims flock to the Da Bo Gong temple to pray and throw coins at the bells around the wishing well (presumably for good fortune, and you can toss a few yourself, too). The deity, also known as Tua Pek Kong, is claimed to have transformed a tortoise into this very island, hence its religious significance. Stalls selling charms and other religious trinkets also set up during the pilgrimage, and it’s the only time food is available on the island.
Besides the temple, there’s a tortoise sanctuary and, if you can manage the 152-step climb up the hill smack in the middle of Kusu, three Malay keramats (which broadly refer to tombs of Islamic ‘saints’) that many believe to grant wealth, health and fertility.
Similar to St John's, getting to Kusu Island is by boat ($18/person for a round trip to St John’s and Kusu), that's available at Marina South Pier.