In pve? Not too many. There are some achievements in LWS1 and LWS2 that give exotic trinkets, but some can only be done once per account.

Frankly, it would be easier to buy LW Season 3- specifically the Bitterfrost Frontier and Bloodstone Fen episodes and farm winterberries with different characters daily, which is enough for a new trinket every few days. All can be bough in Bitterfrost except the amulet, which you can get from Bloodstone Fen.

If you end up buying all of the living world seasons, The “Return To…” achievement offers a convenient way to work towards a legendary amulet while making enough map currency for ascended trinkets along the way.