Complex sentence: The landing of the Army, under General Bonaparte, proceeded well and the French Army scored successes against the Ottomans and the Mameluks; meanwhile, most of the naval squadron was obliterated by the Royal Navy when Nelson caught up, at the Battle of the Nile.
Split into simpler sentences: The landing of the Army, under General Bonaparte, proceeded well and the French Army scored successes against the Ottomans and the Mameluks. However, the Royal Navy, under Admiral Nelson, obliterated most of the naval squadron at the Battle of the Nile.