Integer Interpretator

Python 2, 50 bytes

l=input()
while l:s=set(l);print s;map(l.remove,s)

Try it online!

Repeatedly prints the unique of elements of the list, then removes one of each such element. A rare imperative use of map.

Haskell, 39 bytes

First we collect all equal elements in separate lists using sort and then group. By transposeing the resulting list of lists we get at most one of each of those elements in the resulting lists.

import Data.List
f=transpose.group.sort

Try it online!

Example

                     [1,2,3,2,4,2,1,5] --input
                sort$[1,2,3,2,4,2,1,5] --[1,1,2,2,2,3,4,5]
          group.sort$[1,2,3,2,4,2,1,5] --[[1,1],[2,2,2],[3],[4],[5]]
transpose.group.sort$[1,2,3,2,4,2,1,5] --[[1,2,3,4,5],[1,2],[2]]

Jelly, 3 bytes

ĠZị

A monadic Link accepting a list, which yields a shortest set-wise partition such that each part is a set.

Try it online!

How?

ĠZị - Link: list, L                      e.g. [8,2,4,2,9,4,1]
Ġ   - group indices of L by their values      [[7],[2,4],[3,6],[1],[5]]
 Z  - transpose                               [[7,2,3,1,5],[4,6]]
  ị - index into L                            [[1,2,4,8,9],[2,4]]