"Considerable acclaim" means that something or someone has received a lot of praise, admiration, or recognition for their work or achievement. Full definition
This approach has met with outstanding success and has received considerable acclaim around the world. (closecouples.com)
Since 2004 the British writer / director has made a string of highly original and inventive films, developing his distinctive filmmaking style while winning considerable acclaim. (lwlies.com)
Burgin received considerable acclaim for such work, but over time his relationship to art practice shifted. (4columns.org)