In Glorious Achievement, GA points are given occasionally in 1100, 1125, 1150, 1175, 1205, 1225, 1250, 1275, 1300, 1320, 1350, 1375, 1400, 1425, and 1453, the final year of which is when they're finally totalled up and the side with the highest GA total wins. There is no hard line that has to be crossed, hence your victory can involve overwhelming point gain on your part, or eliminating everyone that does better than you by 1453.
There are three ways to gain GA points:
Homelands is the control of certain provinces which are worth more to you than to all/most other factions. (Some factions share homelands which can lead to angry wars.) In GA Mode, the AI will often make some effort to control its own homelands which may be worth 1-6 points for the relevant faction.
Conquest is the control of any provinces but depending on your faction and the mod you're playing, your homelands may or may not count towards this total. Some of the new factions in XL get conquest points that stack with the homelands points from their homelands provinces. Additionally, there is a maximum cap of 32 points gained through Conquest.
Each faction also has a set Conquest Ratio which determines how many points they get. Some factions have an excellent conquest ratio. Some sides in XL will gain three GA points for each and every province they control, making them very quick to gain these points but absolves them from conquering large tracts of land. Some have more moderate ratios such as 3 points per 2 provinces or 1 for 1, making Conquest profitable but still requiring relatively large scale expansion. Some factions will gain 1 point for every 5 provinces or something similarly bad. Such factions necessarily gain most of their points either by disrupting the point tallies of the leaders or by gaining points through ancillary goals.
In both cases above, it is only necessary to control the relevant provinces on the year of the point tally as noted above. You should still gain the points even if you are at the time sieging an enemy fortress.
The third way to gain points is from various other arbitrary goals set by the game which generally pay some lip service to history. Some factions do not have them at all while some goals are shared, such as the "Iberian Civilization" (shared among the Iberian factions) and the Crusades (shared by all catholic crusading factions). Some factions are very dependent on these if they lack significant points from homelands or conquest while others can get by without them. The new factions in the XL mod do not have these due to programming limitations.
These points will still only be actually tallied in one of the dates listed above but the GA Points menu will indicate so if you're on the way to getting them. On one hand, it is thus not necessary to actually seize those goals prior to those dates. On the other, it is very helpful to plan well ahead of them and shape your game towards those goals.
Playing a GA game still allows you to conquer the map, but gives you a (generally less tedious) alternate victory and allows more room for error since your performance early is (in theory) as important as your performance late in the game. It does however require that you play all the way to 1453 as well as to keep tabs on the point gain of other factions to prevent them from exceeding yours. Additionally, some of the GA points will not be available if you start after Early and some will be much harder to achieve due to having less preparation time. As far as I know, MTW is not balanced to take this into account. Some faction AI's are also naturally better than others at gaining GA points (watch out for the Russians in Late VI).
A final note is that elimination from the game resets any faction's points to 0, even if they subsequently revive. This is the human player's last, most powerful weapon against an AI ahead on points. Having the capability to execute this strategy on any AI faction anywhere on the map will secure victory.
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