The phrase "holds fast" means to firmly grasp or cling to something, and there are many synonyms that have a similar meaning. Some alternative phrases could include "cling tightly," "persevere steadfastly," "maintain a firm grip," "hold tight," "hold steady," or "stick to like glue." Other words that could be used to convey the same idea include "adhere," "cling," "grasp," "grip," "cling on," "stick," or "hold on." These words are often used to describe a person's determination or commitment to a particular goal, as well as their resolve to withstand challenges and difficulties.