I can give help with dom tower since it is an activity I have done a lot of and enjoy.
For the Dominion Marker 4, you need to complete every achievement in the tower. Special matches are all fairly simple [in eoc] but there are guides for each one if you need help.
Probably the hardest part if getting all 20 journal pages, this usually takes 5-10 hours and is achieved by looting the rewards box, the higher your dominion factor the better the chance of getting a page (therefore it is advised to do climber mode). However this should be set against the time it might take to defeat certain bosses.
example gear
example inventory*
This gear pretty much sets you up for every boss. (*It's a good idea to bring your own Balmung for Dagganoth Mother 2). As you ascend the tower you get more and more penalties, it is worth noting that every boss can be defeated with every penalty active, although this will be a time waste and unnecessary risk.
You need to defeat certain bosses to unlock the dominion gloves, but after they are defeated once you are free to skip them.
The sack of potatoes is there to fill your inventory when you get the penalty which un-equips your weapon (if your inventory is full your weapon will not be taken off).
Skip the following bosses:
Pest Queen
Decaying Avatar
Eruni, Ayuni and Leeuni
Zenevivia
Damis, Fareed, Kamil and Dessous
The overarching idea is to get as much dominion factor in the least amount of time for the best chance to get journal pages. It should take you near enough to 500 boss kills - or probably more to attain all pages. If you complete the journal before hitting 500 boss kills switch to endurance mode (more boss kills, less dom factor).
Oh and make sure taunts are turned off.
Good luck & let me know if you need more help with it.