Go through the Collections class and see whether there is any way to sort part of the List. I don't think there is. You can create a sublist, sort that, and copy it back, however.
In Java8 you can probably use a Stream. Maybe something like this:-
myList.stream().sorted().toArray()
…which gives an array. Cast that array to Tweet[] and you can use it to create a List.
There must be a better way to create a List. I shall challenge you to find it. A good source about all things List‑y is the
Java Tutorials, so start there.