How do I integrate Beyond Compare with ClearCase?

As mentioned in my previous answer, just modify the map file located in:

# up to ClearCase 7.0
c:\program files\rational\ClearCase\lib\mgrs

or

# ClearCase 7.1 and more
c:\program files\IBM\RationalSDLC\ClearCase\lib\mgrs

Each map line has 3 parts: the CC filetype, the CC action, and the application.

In your case, find the section in the map file for text_file_delta file types.
There you will find lines for CC actions compare, xcompare, merge, and xmerge.

Use BeyondCompare:

text_file_delta xcompare C:\Progra~1\Beyond~1\bc2.exe  

Beyond Compare 3 support all CC actions:

text_file_delta compare C:\Program Files\Beyond Compare 3\BComp.exe
text_file_delta xcompare C:\Program Files\Beyond Compare 3\BComp.exe
text_file_delta merge C:\Program Files\Beyond Compare 3\BComp.exe
text_file_delta xmerge C:\Program Files\Beyond Compare 3\BComp.exe 

Note: For Beyond Compare 2, this page clearly mentions

To use Beyond Compare 2, only change the xcompare line of the map file.
Overriding compare, merge, and xmerge is not supported.
A helper that improves BC2’s support is available here.

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Note that what precedes is for ClearCase only, not CCRC (ClearCase Remote Client)

This technote illustrates how to change the XML diff/Merge tool for CCRC (KDiff3 but you can adapt it to BeyondCompare):

Change directories to the CCRC installation location > plugins > com.ibm.rational.clearcase.compare_merge.<os>_<ccrc ver>,
Where <os> is the name of the operating system bits used and <ccrc ver> is the latest version of the CCRC update applied on the client.

On Windows

• CCRC 7.1 Default: C:\Program Files\IBM\IMShared\plugins
• CCRC 7.0 Default: C:\Program Files\IBM\Rational\ClearCase\CCRC\plugins\

Example:

com.ibm.rational.clearcase.compare_merge.win32x86_7.0.1.CU02

• Copy the KDiff3 executable from its installation path to the com.ibm.rational.clearcase.compare_merge.<os>_<ccrc ver> directory
• Rename the ccrc_xmldiffmrg.exe to ccrc_xmldiffmrg_orig.exe
• Rename KDiff3.exe to ccrc_xmldiffmrg.exe
• Close and reopen CCRC

CCRC Issue:

When updating CCRC, the plug-in directory com.ibm.rational.clearcase.compare_merge.<os>_<ccrc ver> will change.
The steps above will need to be run again in the new plug-in directory.

Note: You can control when the updates occur by preventing CCRC from looking for updates automatically.
Click Window > Preferences > Install/Update > Automatic Updates and disable automatic updates.