How can I improve my completion score on the first campaign mission?
I can only guess at what you might need to do.
Did you avoid any fights with neutral creatures? Did you defeat every enemy hero? Did you capture every town? Did you own all artefacts and all heroes and all units that were purchasable from your cities?
Perhaps it counts against you if an enemy player kills a monster or uncovers some territory first? I wouldn't expect that 100% is possible on normal difficulty anyway. Perhaps you need to play perfectly in the highest difficulty mode to get higher completion scores.