DBCC CHECKDB grows tempdb to a huge size - Legacy MS SQL Server 2008 R2 Instance
Actual serious although unusual suggestion: drop all the indexes in the database - or some of them - then "DBCC CHECKDB" has fewer things to check.  Of course you can put them back after...

Alternatively, rebuilding indexes may produce a simpler arrangement of data for CHECKDB to analyse...  this is actually a guess, but you may use fewer pages to store a table, at least.

https://technet.microsoft.com/en-us/library/ms176064(v=sql.105).aspx
describes several WITH options which increase or decrease the workload of CHECKDB, and another option ESTIMATEONLY which causes it do skip any checking but tell you how much space in tempdb is required for checks.  It's implied that this varies when you set other parameters with ESTIMATEONLY  i.e. TABLOCK, PHYSICAL_ONLY.  These do skip some checks.

Most but apparently not all of the checks in CHECKDB can be run as different commands, as described.

https://www.mssqltips.com/sqlservertip/2399/minimize-performance-impact-of-sql-server-dbcc-checkdb/
has  performance-related suggestions including restoring the database backup to a different server to be checked.  This too might not be a perfect check if the restore server is running a later SQL Server version and quietly "fixes" flaws of the original database during restore, so that you don't see them in the copy.