Is there a chengyu to mean "walk with one's own legs"
I collect the following phrases that have the meaning of "independent".

出道
出师
自立
自立门户
自作门户
独当一面
独立自主
自食其力  

self-reliant
self-supporting
support oneself
support oneself by one's own labor
earn one's salt
earn one's own living
live by the sweat of one's brow
live by one's own labor
live on one's toil
live on the earnings of one's own work
stand on one's own feet  

I think 自食其力 is closest to "to walk with one's own legs".