Achievement refers to the level and status achieved in learning and professional skills.
Perfection refers to perfection in skills or knowledge, or proficiency in doing things. Be accomplished in a certain field.
Calligraphy attainments reach perfection, which can also be manifested as the peak of calligraphy attainments or the superb calligraphy attainments.
Purity means purity, and this word is interpreted as: Taoist alchemy believes that it is successful to make a pure blue flame in the furnace, which is used to describe that a certain field has reached the state of perfection.
The words in the near sense are: dexterity, proficiency, superb, fluency, arrogance, and reaching the peak.