The Millet Bird Sanctuary Trail is one of the best introductions to Saint Lucia's rainforest, with a managed route through forest that gives realistic chances of seeing endemic birds. The Saint Lucia parrot is the headline species, but listen too for warblers, black finches, and the layered sound of the forest.
Go with a guide if bird identification matters to you. The trail is not extreme, but humidity and mud can make even short distances feel longer than they look on a map.