A cotton cultivar designated PHY 78 Acala is disclosed. The invention relates to the seeds of cotton cultivar PHY 78 Acala, to the plants and plant parts of cotton PHY 78 Acala and to methods for producing a cotton plant produced by crossing the cultivar PHY 78 Acala with itself or another cotton variety. The invention further relates to hybrid cotton seeds and plants produced by crossing the cultivar PHY 78 Acala with another cotton cultivar.