Since Arena will be closing on March 10th 2022, I thought I'd put this guide out that I used when going for the arena achievements about a year ago.
The legit way of course, is to get a crew of people together, who are good at pvp, boarding, sword/gun meta and all that stuff. An arena match takes 12 minutes, and asuming lobby wait times, and a win rate of, say, 50%, would take you probably at least 50 hours to accumulate 100 victories. It's a long grind, and if you want to reach Sea Dogs reputation rank 50, even longer.
Thankfully, there's an easier way. On consoles, you have the option to opt out of crossplay. 99% of players in Arena play on PC, because of the obvious advantages of high frame rates, higher resolution screens and M+KB input. As a result, Xbox Arena is pretty much dead. If you can get 10 people together, you should match up with each other in closed sloop crews in Xbox Arena, and grind matches to trade wins, and almost never match up with other players, let alone PC players.
But there's an even easier way! There is an undocumented trick to get into a closed galleon arena match by yourself (normally this would require a full crew) by pressing A+B on the 'Confirm and Assemble' screen (instead of just A), and then A again to enter a lobby. If you get a group of just 5 people together, you can fill a lobby with 5 galleon 'crews' of 1 person each. The game will detect that the lobby is full, and start the countdown - the announcer will say 'Crews! To your ships!'. At this point, designate 1 crew the losing ship, 1 crew the winning ship, and have the other 3 crews quit out and join the winning ship. The match will start, with only 2 ships on the map. One is the losing ship (with 1 person on it), one is the winning ship (with a full 4-person crew on it). Now have the winning ship get some points, and either wait out the 12 minutes, or have the losing crew quit out and forfeit the match. If you decide to wait, you can also work towards a lot of the Arena commendations for digging up chests, stealing chests, getting weapon kills, etc.
Note: quitting out more than a few times will give a temporary suspension that starts out at 30 minutes. You could risk it if you have enough dummy accounts, but I wouldn't recommend it for your primary account.
Using this method, and playing 6-10 matches per day, we were able to grind out everyone's 100 wins in about 2-3 weeks.
tl;dr
* get 5 people together (including yourself)
* turn off crossplay in Matchmaking options
* have everyone go to Arena > Galleon > Closed crew by themselves
* press A+B on the 'Confirm and Assemble' screen instead of A
* press A again to load into a lobby
* you should all match up together as 5 "galleon crews" in 1 lobby
* designate 1 person the losing crew, and 1 person the winning crew
* once the announcer starts the countdown, have 3 crews quit out and join the winning crew
* the match starts with just 2 ships in it, the winning and the losing crew
* losing crew quits out or loses on purpose, giving the winning crew the victory
* repeat 100 times
thatNoseyParker notes that you can do this method with just 4 people, and letting the match start with just 1 crew when the countdown starts. This ensures that there is no 'losing crew' that has to quit out for the match to end early - the match will end instantly since there is only 1 crew. It might take a few minutes longer for the lobby to start into a match, so I'm not sure if this method is faster.