Flight instructor reported a class C airspace incursion.

Narrative:

After completing an IFR flight with student to the ZZZ1 airport; we canceled IFR on short final and requested a tower to tower departure to ZZZ2 with intent to request the published hold at ZZZ VOR. The airspace was very congested with VFR training airplanes.we were given a frequency change to ZZZ2 tower by the ZZZ1 tower controller; and the student; under the hood continued his climb while I attempted to contact ZZZ2 tower; which was extremely congested.after several attempts; I instructed the student to turn to a heading of 150 and level off prior to 2;700 MSL to exit the local airspace and was focused outside. Due to the heavy training activity; I could not contact ZZZ2 tower.I looked inside and noted that the student had climbed to above 2;900 MSL which was inside the class C shelf of ZZZ; but nearly clear to the south.I instructed the student to level off and depart the airspace; and we returned to our home base without further incident. In retrospect; due to the congestion; I would have landed at ZZZ1; taxied to the ramp; and amended my plan with the student. Traffic congestion since covid has been significant; and has made training IFR training a challenge. I have begun to mitigate this by filing direct to airports as previously described with a plan to return home under VFR. In the future; I will no longer request tower to tower and plan to leave and attempt holds at airports in northern ZZZ3 county.

Original NASA ASRS Text

Title: Flight Instructor reported a Class C airspace incursion.

Narrative: After completing an IFR flight with student to the ZZZ1 airport; we canceled IFR on short final and requested a Tower to Tower departure to ZZZ2 with intent to request the published hold at ZZZ VOR. The airspace was very congested with VFR training airplanes.We were given a frequency change to ZZZ2 Tower by the ZZZ1 Tower Controller; and the student; under the hood continued his climb while I attempted to contact ZZZ2 Tower; which was extremely congested.After several attempts; I instructed the student to turn to a heading of 150 and level off prior to 2;700 MSL to exit the local airspace and was focused outside. Due to the heavy training activity; I could not contact ZZZ2 Tower.I looked inside and noted that the student had climbed to above 2;900 MSL which was inside the Class C shelf of ZZZ; but nearly clear to the south.I instructed the student to level off and depart the airspace; and we returned to our home base without further incident. In retrospect; due to the congestion; I would have landed at ZZZ1; taxied to the ramp; and amended my plan with the student. Traffic congestion since COVID has been significant; and has made training IFR training a challenge. I have begun to mitigate this by filing direct to airports as previously described with a plan to return home under VFR. In the future; I will no longer request Tower to Tower and plan to leave and attempt holds at airports in northern ZZZ3 County.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.

Attributes
ACN	1765150
Time
Date	202010
Local Time Of Day	1201-1800
Place
Locale Reference	ZZZ.Airport
State Reference	US
Environment
Flight Conditions	VMC
Light	Daylight
Aircraft 1
Make Model Name	Small Aircraft High Wing 1 Eng Fixed Gear
Operating Under FAR Part	Part 91
Flight Phase	Climb Cruise
Route In Use	Direct
Flight Plan	None
Person 1
Function	Instructor
Qualification	Flight Crew Instrument Flight Crew Flight Instructor Flight Crew Air Transport Pilot (ATP) Flight Crew Multiengine
Experience	Flight Crew Last 90 Days 100 Flight Crew Total 5200 Flight Crew Type 700
Events
Anomaly	Airspace Violation All Types Deviation - Procedural Published Material / Policy Deviation - Procedural FAR