Quite simply, go to any outpost around the map with someone from another ship and get drunk together. Thanks to those in the comments confirming that you only need be on the island and not in the tavern. I was in a tavern when I completed the achievement.
Obviously, the tricky part is finding someone who won't shoot first and ask questions later. I encourage you to play with a headset and be in game chat if you are playing with a crew as you can communicate with other crews in close proximity to you.
AStarfox recommended in the comments that if you don't have a mic that you can use the in-game text chat to talk to anyone from another crew in close proximity. This will work on Xbox or PC in crossplay. If you're on Xbox and have a keyboard or chatpad attached press T to bring up the chat prompt. Xbox Only lobbies disable attached keyboards + mice on Xbox, so having a mic is almost required.
Here are a few of my suggested ways to show you come in peace while trying to make friends on the seas. As new mechanics are introduced into the game, I will update the below list. Sorry that it might become a bit of a read.
Warning Everything mentioned can obviously have someone approach you pretending to be a friendly only to betray you in true pirate fashion.
1. Leave the lights on your ship on.
2. Aim your cannons up towards the sky. This shows you do not intend on shooting others.
3. Use the speaking trumpet (megaphone) to talk to people further away. The max distance is hard to explain, but basically if they are close enough that when looking through the spyglass to see their character model they can hear you with the trumpet. Be smart about what you say and maybe start off with "I am trying to get achievements, could you assist me?" Also, this should go without saying but they only hear you if you hold the trumpet to your mouth. LT on controller, right click on PC.
4. Don't pull out weapons. Duh! (Exception would be to block attacks with the sword while verbally telling them your intent.)
5. If the ship is actively avoiding you or shooting at you, stay away. They might have loot or are fish for Hunters Call.
6. Go into your crow’s nest and throw up the alliance pendant. Doesn't always work but it's worth a try.
7. The smaller the ship the less of a threat you present to others. Not saying there are not some awesome Sloop only players who can wreck Galleons, but a Sloop approaching a Galleon might get a chance to talk before being fired upon.
8. DO NOT approach in a rowboat. Trust plummets since rowboats are a great way of kegging a ship without the mermaid giving away your position.
9. This is not needed but can sometimes help. Bring a gift/payment/bribe. I recommend cursed cannon balls but have a chest or skull as a backup. Keep the cannon balls on you so there is incentive to not kill you and skink your ship.
Last but not least you will find salty or even toxic players in Sea of Thieves just like every other game out there. Some of these players hide behind a flawed logic of "the game is called Sea of Thieves not Sea of Friends." While correct, it is not Sea of Toxic Behavior. The word Thieves in their mind means be obnoxiously rude and constantly attack players (or even hunt down the same ship over and over) even when they have nothing of value (loot) on the ship. If you come across toxic players don't let them get on your nerves as that is what they want. Rather tell them to have a nice day and switch servers. Do note that the difference between toxic and a player actually being a Pirates in the game can be a gray area as sometimes people are tucking on your ship to steal your loot later or trolling for the laughs. Basically it is very subjective and just don't go reporting every person that boards your ship. Sometimes some civil communication can clarify the situation.
Here is an incomplete list of a few other achievements you can get along with this one while having the help of another random person/crew. The first one will require at least 5 people.
The Hold My Grog! achievement in Sea of Thieves worth 144 pointsLaunched from your vessel, this cannon-fired trip must see you land safe on the deck of a ship!
The Tactical Chunder achievement in Sea of Thieves worth 112 pointsWhen threatened at sword point, remember this trick: blind your poor foe with a bucket of sick!