If a large figure exits a blue square and enters another blue square while stepping on the previous blue square (so it lands on 2 blue squares) - how many movement points are necessary? Just 2 or more?

RRG, Difficult Terrain said:

· When a large figure enters difficult terrain, it spends only
one additional movement point, regardless of the number of
spaces of difficult terrain that it occupies.

Also, only the spaces a figure enters matter when determining the movement point cost.

FAQ3.0

Q: When a large figure moves, does it exit all spaces it
occupied and then enter all of its new spaces, even if some of
those spaces overlap?

A: Yes.