Here are some things you can do to add a sense of hopelessness:
- Add a guy (or several) with guns—increase the power of the antagonistic force
- Reveal (and polish up) the master plan of the hero's foe—make it as impossible to stop as possible
- Make the antagonist more ruthless—kill some of the hero's friends...
- Deprive the hero of support towards the end so that s/he is facing off the final "boss level" all alone
However, it's more important that the reader feels there is no hope than that the hero does.
A hero that says, I don't care if it's impossible, I'm going to do it anyway will likely also get lots of reader sympathy.
What you can do, however, is to add a midpoint mirror moment where a hero that goes through a change will ask themselves "who am I? why am I this way? why am I doing this to the people around me?" while a hero that does not change (or follows a flat arc) has more of a mirror moment along the line "I'm probably going to die." (See "Write Your Novel From The Middle: A New Approach for Plotters, Pantsers and Everyone in Between" by James Scott Bell)
This happens in the middle of the story and it can be a low moment, but usually, the midpoint represents a realization that the current strategy isn't working and motivates the hero to change things up (e.g. go from reactive to proactive, go from believing in a lie to believing in a truth, realizing some important stuff about the conflict, the antagonist, themselves or all of the above...)
You can usually increase the sense of hopelessness by making the events that happen to the hero more horrible. To do that:
- Move the event physically closer to the hero (e.g. from "hearing about some horrible event" to "being the victim of a horrible event")
- Make the hero more responsible for the events
- Repeat the events more than once
- Pile on other events that might logically follow the event (divorce, getting fired, anxiety attacks, depression, other people injured, etc)
- Make the antagonist emotionally closer to the hero (e.g. from a total stranger to the hero's parent...)
- Tailor the event to the hero's personality or emotional state
(See "The Emotional Wound Thesaurus: A Writer's Guide to Psychological Trauma" by Becca Puglisi and Angela Ackerman)