lumbering up the steps
plodding past me
The two verbs used to describe the way the giant tortoises move are "lumbering" and "plodding". Both of these verbs carry the connotation that something very large is moving awkwardly. Plodding refers to the loud sound it would make when its feet hit the ground, and lumbering describes the awkward way limbs move when they're so big and heavy.
