By Alexander Gladstone 

$AMC Entertainment(AMC.US)$ is stepping up its efforts to refinance some of its debt as the cinema chain's shares and bonds have slumped, giving up most of their gains since the company became a meme-stock favorite.

AMC is in advanced refinancing talks with multiple interested parties, according to people familiar with the matter who said the company has options to lower its interest burden and stretch out maturities by several years.

Chief Executive Adam Aron said earlier this year that in 2022 he would like to refinance the expensive debt the company took on to outlast the pandemic. The selloff in AMC's bonds might make refinancing more difficult, especially as the Federal Reserve prepares to raise rates, according to financial analysts.

AMC's stock has declined by 41% this year through Tuesday's market close, a steeper drop than the broader market selloff hitting stocks and cryptocurrencies. While the company's bonds had previously held up even as its shares slipped, on Monday the bonds dropped by several points. That indicates that even creditors, who enjoy a greater degree of protection from losses than stockholders, are getting skittish about the business.

AMC isn't targeting all of its debt stack for refinancing, just some of its bonds that carry especially high interest, one of the people familiar with the matter said. Even if the decline in AMC's bond prices caused their yields to rise, the company may still be able to strike a deal that would cut interest expense compared with what it pays now, the person said.

AMC had $5.5 billion of debt as of September that ranks ahead of the equity, including high-interest bonds, and owed $376 million of lease payments that were deferred during the pandemic.

On Tuesday, AMC's $1.5 billion in secured 10% bonds due 2026 traded as low as 92 cents on the dollar, down from 99.5 cents at the start of the year. Another bond with less collateral protection traded as low as 69 cents on the dollar on Monday, down from 72 cents in early January, according to MarketAxess.

In early 2021, AMC became a darling of individual investors, many of whom refer to themselves as the apes. They helped push AMC's stock price to eye-popping heights through meme-heavy social-media hype, and they came to own more than 80% of the company.

"At first it was a very well-defined and purposeful anti-Wall Street type movement," said Chad Beynon, an analyst at Macquarie Group Ltd., regarding the ape community. "That story is no longer as attractive. After seeing it not working for a few months, there's some sort of fatigue."

AMC, as well as its peers in the cinema business, continue to struggle with getting customers into their theaters as the pandemic drags on. While the film "Spider-Man: No Way Home" was a recent hit for the theater industry, box-office revenue for the latest weekend amounted to a mere $46 million, compared with $123 million the same weekend in 2020, and $104 million in 2019, according to Comscore data.

Since the Covid-19 pandemic began, AMC has stayed alive by a combination of selling new shares, taking on new debt and getting landlords to agree to delay collecting rent payments. But the apes' takeover of AMC has restricted its options for dealing with the debts it took on to get through the worst of the pandemic lockdowns.

Last year, AMC twice failed to win shareholder approval of new equity issuances as apes fretted about dilution, despite Mr. Aron lobbying to allow for more shares to be sold. Now the company isn't able to issue stock to pay down debt, said Michael Pachter, an analyst at Wedbush Securities.

"The shareholders blew that," Mr. Pachter said.

Despite the sliding share price, some apes are holding on, viewing their commitment to AMC as an act of defiance against the hedge funds and Wall Street institutions that bet against the stock by short selling it. The ape community has also become a forum for opposition to a financial system they believe stacks the deck against individual investors.

Anton Torres, a cable technician in Washington state who bought stock in AMC last January, said that he and the other apes he knows are holding on to their shares because they believe that AMC's stock price might rise again.

"I'm holding hoping the value increases, but I'm also holding because it's bringing awareness to a system that is poorly regulated and I like the stock," Mr. Torres said.

Write to Alexander Gladstone at alexander.gladstone@wsj.com