There are various degrees of beating it. The original story ended when you defeated the Shadow Lord and achieved Rank 6. Or you could consider a level 75 character and attaining Rank 10 with your home nation as beating it. Or you could do that and also the expansion storylines, one of which hasn't been completed yet.

This is what I would consider 'beating' FFXI in terms of story:
Attain Rank 10 with all three nations.
Complete the Rize of the Zilart story missions.
Complete the Chains of Promathia story missions.
Complete the quest Apocalypse Nigh which ties the RoZ and CoP expansions.
Complete the Treasures of Aht Urhgan story missions.
Complete the Wings of the Goddess story missions. (unfinished)
Complete the Wings of the Goddess nation quests for all three nations.