Drink From The Puddle At The Starting Camp Repeatedly, With the Jar From The Supplies Box.
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You Will Get Random Diseases From This Dirty Water, pretty much 9 times out of 10.
Once You Get All The Big Ones, (Like Dysentery) You Will Be Able To Stack More And More Parasites, And You Will Not Die Because Their Dehydrating Effects Won't Take Effect Until You Leave The First Island.
It Will Seem Like You Arent Getting More Diseases After A While, But It Is Just Rolling Diseases You Already Have, And Can Not Stack.
Once You Have 10 Diseases, The Achievement Pops.
Then Do Yourself a Favor And Get On Your Boat, And Do This Achievement.
Goodluck!