Just full-hop bair them off or hold jab if you're a little ways away - jab is really good for it, bair is fine, and you can also try skull-bashing away from your opponent (that may be electric-type though, I'm not sure). Fair is good if they have no yellows in the lineup, as is dair, and it's still better to knock one or two off than not fair because you're worried you don't remove them all. Uair is fine too, it just takes more uairs to shake off most Pikmin (Except white ones, they should die to one uair most of the time).
Nair is good for removal when Olimar is at low percents because it should be destaled (9 or 10 hits) by the time he's at KO percents (unless he keeps walking into sweetspot fsmash, at which point you probably don't need to worry about a stale nair if you land sweetspot fsmash over and over again).
There's 2010 footage of Anther vs a few different Olimars (no names I recognize). The MU looks pretty awkward for Pikachu, despite Anther's smooth play (and when I played an Olimar in tourney [I won game 1, lost game 2, and went Falco game 3 for the win] it felt weird trying to get in).