To fight him you either CC him in human form NOT Raven form and burst him down or you fight by kiting back so he cannot heal himself, here is his ultimate (R) tooltip;
Swain inspires dread in his enemies by temporarily taking the form of a raven. During this time ravens strike out at up to 5 nearby enemies. Each raven deals damage and heals Swain for a portion of the damage dealt.
Toggle: Swain transforms into a monstrous raven, spawning up to 5 lesser ravens per second that strike out at nearby enemies, prioritizing champions. Each raven deals 50/70/90 (+20% Ability Power) magic damage and heals Swain for 30/45/60 (+0) against champions and 8/11/14 (+{{ f10 }}) against minions and monsters.Ravens can't attack the same target for 1 second and the mana cost to sustain Ravenous Flock increases by 5 Mana each second.
His Q the zone which he puts out with a Raven increases his damage so watch out for this too in a combo.
Now you cannot fight a swain stacked on top of him if he has items and is relevant he WILL out sustain the damage and heal himself it's literally what he is built for, for a different team dynamic and type of apc.
If he is fed and you have no cc in your team then kill him by kiting back his Ravens are pretty short range in the Raven form.
And just a FYI he was as powerfull as this pre update people just didn't look at him much.
Edit; it's worth to note that if he zonyas his ult carries on damanging and healing through it