The total amount of Qaza prayers for each day is only 20 cycles.
Niyyah (Intention)
Niyyah (intention) for Qaza Salah can be performed in the following manner:
Say you have 100 Fajr Qaza. Every time you perform one Qaza, say, "I intend to perform my first Fajr Qaza". In this way you will perform them all. The same method can be used to complete all salah.
Easier Method for Large Numbers
If someone has a very large number of Qaza that he must fulfill then he may also do the following things to make it easier for him:
1. Ruku and Sajdah Tasbeeh
Instead of saying 'Subhana Rabbi al-Azeem' or 'Subhana Rabbi al-A'ala' thrice in Ruku and Sajdah, you may say it just once.
[It is of paramount importance that in all types of prayers that: you only start reciting 'Subhana Rabbi al-Azeem' or 'Subhana Rabbi al-A'ala' once you fully enter Ruku or Sajdah and only leave Ruku and Sajdah once you completely finish reciting them.]
2. 3rd and 4th Cycles
In the 3rd and 4th cycle of Fard Salah, pray Subhan-Allah three times instead of Surah al- Fatiha but remember to pray it completely whilst standing up before going into Ruku. [In Witr, one must recite Surah al-Fatiha and a Surah in all the cycles.]
3. After Tashahhud
After reciting al-Tahiyyat, instead of Durud Ibrahim and Dua Mathoora - just recite 'Allahumma Salli 'Ala Muhammad' then end Salah.
4. Witr Qunoot
In the 3rd cycle of Witr, after the Takbeer - pray 'Ya Rabbi-gh'fir li' once or three times, instead of Dua-e-Qunoot.
Important Notes
One can read Qaza Salah anytime outside of the Makruh (disliked) times, which are:
One must also perform this Salah in secrecy, as the exposure of sins in public is not permissible.
Note: The Qaza of any Salah missed while travelling will also be shortened e.g. If the Zuhr Salah was missed while traveling, then the Qaza Salah for it would also be 2 rak'ats.
References: Bahar-e-Shari'at, al-Malfuz & Fatawa Ridawiyyah (Imam Ahmad Rida Khan & Imam Amjad Ali Azmi)