Do new SIGHASH types need a hard fork or a soft fork?
It is in fact a hard fork, if it is done natively. However, it can be done through a soft fork if the sighash types are only included in serialized redeemScripts for P3SH (P2SH but with OP_EQUALVERIFY instead of OP_EQUAL), or via re-purposing one of the OP_NOPs to be a new op with similar functionality to OP_CHECKSIGVERIFY.

Source: http://lightning.network/lightning-network-paper-DRAFT-0.5.pdf


  To mitigate malleability, it requires changing which contents are signed by the participants. This is achieved by creating new Sighash types. In order to accommodate this new behavior, a new P2SH type or new OP_CHECKSIG is necessary to make it a soft-fork rather than a hard-fork.