The Burgundian Conquest
Burgundy starts off in quite a difficult position, being wedged in between France and the members of the Holy Roman Empire. The Burgundian army in itself is smaller than that of France, and cannot tackle the armies of the Emperor head on either. Also, Burgundian manpower is often low and reliance on mercenaries can thus be needed. Luckily, Burgundy has much needed help from their subjects Nevers, Holland, Brabant and Flanders. With the support of its subjects (tip: set the subjects to supportive warfare mode and allow attachment to your army), Burgundy should strike at enemies when a good opportunity arises, such as when France is busy battling England/ Castile/ Aragon or when the Emperor of the HRE battles the Ottoman Empire. Conquering the French areas, with possible additional help from Castilian or Aragonese forces, is a good way to start developing Burgundy into a strong continental power. The trade power of provinces such as Champagne will benefit Burgundy a lot. The English provinces of Normandie, Caux and Calais can also bolster the Burgundian economy additionally, and taking them before the French have the possibility to do so should be considered by the player.
It is important to remember not to take too many provinces at once, as an early coalition against Burgundy can be devastating and set back the progress of the player a lot as France then has time to regain its power.
Handling of subjects and integration
By the time that the player has started to gain the advantage against the French due to the French losing the majority of their provinces, integration of the Burgundian subjects can be done safely as Burgundy now should be able to rely on its own forces. Integration of the Burgundian subjects also frees up diplomatic slots that can be used to secure valuable alliances. All of the subjects have quite high development, but since Holland also has a center of trade and an estuary it is advisable to integrate them first, as the trade income will be a welcome addition to the Burgundian treasury.
When France has been diminished to a size where they can be vassalized, the player should consider if they want France to be able to support troops for Burgundian wars in Europe (as French troops have high morale), or if France should be diminshed to such a small size that they could never efficiently rebel against their new overlords as France then would have too low of power in comparison to Burgundy. Whichever option the player prefers, they will both have upsides and downsides.
Depending on what has happened up to this point in the campaign Austria can either have become very strong due to their position as Emperor and possible senior partner of unions with Hungary and Bohemia, or have been weakened because of losing the Thirty Years' War or failing in their duty as emperor of the HRE. If Austria has become weakened Burgundy can probably take them on with the help of their newly gained power and wealth stemming from the conquered French regions, as they are generally very high in development. If Austria is powerful a more careful approach should be taken by the player however, and Burgundy should look for alliances with strong Austrian rivals. The Ottomans usually rival Austria, and can be very helpful with their high amount of troops if an alliance is gained with them. If the Commonwealth or Muscovy/Russia exist they can also work well as strong allies.
The best solution to deal with Austria without becoming a target of coalition is to take only a province of Sundgau in the first war and immediately release Styria as a vassal. This would get the player reconquest casus belli, which would allow indirectly conquering most of Austrian starting territory in a single war, despite lacking a land connection. Another approach is to take the Austrian provinces which are bordering the Adriatic Sea, but conquering Austrian provinces directly would result in huge aggressive expansion combined with Emperor demanding the unlawful territory from the player.
When Austria has become reduced to a size fit for vassalization the player should do so. The decision between keeping them small and loyal or larger and more helpful in battle is not as important any longer, as Burgundy now probably has become one of the stronger, if not the strongest, power in Europe.
The Low Countries
The Low Countries should probably, after integrating the Burgundian subjects, consist of Burgundy and a few small nations such as Utrecht, Liege, Friesland, Gelre and East Frisia - do note that East Frisia is not a HRE member, so it is possible to pick off allies to it. Those countries can advisably be attacked at opportune moments when the Emperor of the HRE is busy with other wars or when the Emperor is weakened by other circumstances. Aggressive expansion will surely rise after annexing said countries, which should be kept in mind by the player.
Rebels will spawn at intervals in the Low Countries in the years between 1550 and 1650 (See dutch revolt events). Said rebel armies can be quite large, usually consisting of around 50k troops. Burgundy should therefore always be ready to strike down any revolts in the Low Countries during aforementioned period of time. This can be avoided by moving your capital to the region.
Burgundy have some idea groups that synergize well with their position in Europe and their national ideas. The quantity idea group can serve Burgundy well with the extra needed manpower. After conquering France Burgundy will have high trade power in two end-trade nodes, which the trade idea group bolsters even further, creating a large income to support the large Burgundian army. The influence idea group is also good for handling the different Burgundian subjects and avoiding aggressive expansion. Since many Burgundian national ideas deal with mercenaries, administrative ideas synergize well, and also provide lower coring costs, which is welcome for the many high development provinces Burgundy will be taking.
Burgundy is unique because they can reform both into France and the Netherlands. This should not be done by the player while trying to get the achievement however, as Burgundy is needed to fulfill the achievement criteria. Luckily, when Burgundy upgrades its government rank into an empire it gets a cultural union with all the French cultures, making all of said cultures accepted in Burgundy. Alternatively Burgundy can form Lotharingia via its mission tree and this is the only country formation which doesn't prevent the achievement.