Short answers, pulled from the story.
An achievement is a full display of all heraldic components forming the entire visual statement granted to a bearer of arms. This term covers the central escutcheon surrounded by many other elements including mantles, crests, and supporters.
John Russell 1st Earl of Bedford installed his plate on the 18th of May 1539 when he became a Knight of the Garter. The design included specific badges like the ostrich feather shown as a pair with argent pen gobonne argent and azure colors.
King Henry VIII issued statutes concerning the regulation of Garter stall plates to dictate how knights of the order presented their visual symbols. These rules ensured that the visual presentation remained under strict royal oversight throughout history.
Specific social ranks determine which components are entitled to be used because holders higher than a baronet may issue from a coronet or crown instead of a simple helm. Baronets generally do not use supporters in modern usage despite holding high status while entitlement exists for others by law or grant.
The ancient term used in place of achievement was hatchment which derives through historic forms like atcheament, achement, and hathement from the French verb achever. This phrase traces back to Latin ad caput venire meaning to reach a conclusion before becoming exclusive to funerary contexts in modern English.