The oil tank side has 2 openings in the top of the cover which fit over 2 'studs' to hold it in place. These studs hold the cover in place, unlike the worthless 'pressure fit' method on the battery side.
To get it off you need to gently
pry the top of the cover so the openings will clear the studs. Easy to bend the cover, so do it carefully.
You might be able to see these 2 holes in the below picture.