There is no achievement system like Java version in the game.

Thank you for your report!
However, this issue is Invalid.

You reported a parity issue. We are only tracking parity issues that meet the following criteria on this bug tracker:

• The feature affected by the parity issue is present in both Bedrock Edition and Java Edition in the latest release or development version

• The feature behaves differently in one edition than in the other

• The parity issue was introduced in Buzzy Bees (Bedrock Edition 1.14 / Java Edition 1.15) or later and was not present before

Any parity issue that does not meet these criteria are not tracked on the bug tracker and should instead be reported on the Feedback website.

Quick Links:
📓 Bug Tracker Guidelines – 💬 Community Support – 📧 Mojang Support
📓 Project Summary – ✍️ Feedback and Suggestions – 📖 Game Wiki