I've been mostly legging when I saw them anyway, but here's some tips on dealing with shields:
1. Massed firepower helps. Shields have no armor value, so no matter what you use, eventually it'll bring the shield down. Easiest way to do so is, in fact, using shotguns - lots of pellets, lots of hits, damage adds up easy shield stripping.
2. Shields take 250% damage from EMP.
3. Lastly, some damage types flat-out ignore shields, in case of star gods (type 3 shields) it's only bio, charm, choking and anti-e511. Bring poisoned knives and cobra staves.