Only a standing 'Mech can receive partial cover from terrain. Even though Large Support Vehicles, grounded small craft and grounded DropShips rise more than a single level above the underlying terrain of the hexes they occupy, they never receive partial cover.
To receive partial cover, a 'Mech must be adjacent to a hex one level higher than the level of the underlying hex it occupies, and that hex must lie between it and the attacking unit. For example, a 'Mech standing on Level 0 terrain is at Level 2 for determining LOS. An adjacent Level 1 hex lying between the attacker and the target would provide partial cover. The firing unit must also have an LOS level equal to or lower than the defending unit’s LOS level in order for the target to receive partial cover. In other words, an attacker firing downhill regardless of how many hexes lie between attacker and target) negates its target’s partial cover.
The intervening level can be a hill, a building (but not a bridge, which does not provide partial cover), a DropShip or any combination. Partial cover does not block LOS, but it adds a +1 modifier to the attacker's to-hit number. The attack is then resolved normally, but if the hit location roll indicates a leg, the attack strikes the cover instead. If the partial cover is a building or grounded DropShip, the hit damages the building or DropShip. See Buildings and Attacks by Grounded Aerospace Unit respectively. For four-legged 'Mechs, a leg hit means any leg at all, front or rear.

ProtoMechs: Because they are only the height of vehicles, ProtoMechs never benefit from partial cover.

Woods: A 'Mech does not receive partial cover from woods.