The leaderboard is split into three sections: overall score, PvP score, and Respect. Overall score is just the combined totals of your PvP score and Respect score.
Respect score is split between Advancement, Army Size, and Battles score.
The Advancement Score is based on number of completed Research projects, the amount of licenses owned, and the number of medals earned. Complete more research, acquire licensed units, or earn more medals to increase your Advancement score.
Army Size Score is based on the Deployment Cost of all units you have, whether they are in Storage, or involved in a raid or smuggling mission. Acquire more units to increase your Army Size score.
The Battles Score is based on the total number of battles won against the AI. Play and win more raids, boss battles and smuggling defense missions to increase this score.
PvP Score is based on successful PvP wins, and the level of the opponents fought. To increase this score most effectively, battle the same or higher level players and win.