Joseph Achron, known primarily for his violin works, utilizes a more modern, coloristic harmonic palette in this Berceuse. It is distinguished by its chromaticism and sophisticated textural layering.
Mastering the subtle shifting of harmonic colors requires advanced control of the damper pedal.
Comparable difficulty and character — good candidates for what to learn next.
Berceuse No.2 (Op.20) is rated Henle level 5 of 9 — late intermediate repertoire, roughly ABRSM grades 6–7. In the RCM system it corresponds to about level 7.
You should be comfortable at Henle level 5 — meaning you can already play level 4–5 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of Berceuse No.2 (Op.20) lasts about 4 minutes.
Berceuse No.2 (Op.20) is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include Gymnopédie No. 1 by Erik Satie, Berceuse élégiaque, BV 252a by Ferruccio Busoni, "Esquisses hebraiques" by Alexander Abramovich Krein — see the full similar-pieces list on this page.