これを試してください
$this->db->select('*');
$this->db->from('adm_species t');
$this->db->join('adm_breeds e', 'e.species_id = t.id');
$this->db->join('fd_registrations s', 's.breeds_id = e.id');
$this->db->where('t.code', 'cat');
$this->db->where('s.sex_id', 2);
$this->db->like('s.ownername', 'sha', 'both');
$query = $this->db->get();