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Subsequent Events (Additional Information) (Details) - Subsequent event [Member] - June 2025 Public Offering [ Memer] - Underwriting Member	Jul. 25, 2025 $ / shares shares
Subsequent Event [Line Items]
Additional number of shares to be issued as option in part | shares	1,419,896
Sale of common stock and warrant, public offering price | $ / shares	$ 3

X

- Definition

Sale of stock, additional number of shares to be issued in transaction.

+ References

No definition available.

+ Details

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Namespace Prefix:	achv_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

X

- Definition

Per share amount received by subsidiary or equity investee for each share of common stock issued or sold in the stock transaction.

+ References

No definition available.

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

X

- Definition

Detail information of subsequent event by type. User is expected to use existing line items from elsewhere in the taxonomy as the primary line items for this disclosure, which is further associated with dimension and member elements pertaining to a subsequent event.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 830
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481674/830-30-50-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 855
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483399/855-10-50-2

+ Details

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Balance Type:	na
Period Type:	duration

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- Details

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Namespace Prefix:
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Period Type:

X

- Details

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Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=achv_UnderwritingMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: