Small Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 27; Flight Crew Total 9500; Flight Crew Type 1465
Distraction
Deviation - Altitude Crossing Restriction Not Met; Deviation - Altitude Undershoot; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Fuel Issue
Air Traffic Control Provided Assistance; Flight Crew Requested ATC Assistance / Clarification
Human Factors; Environment - Non Weather Related
On flight from ZZZ1 to ZZZ2; which was at the limit of our aircraft range unless there are decent tailwinds; had a hard time getting a climb; barely any tailwinds and was expecting a cumbersome arrival.  So; when we were over West [State] and assigned the ZZZZZ arrival I was wondering if we would land with minimum IFR reserves.  Asked Center to keep us high as long as possible and they did a pretty good job except this involved lots of vectors and altitudes when getting closer to ZZZ.  So; during descent I was delaying a steep descent until closer and lower to save fuel.  All of this ended up working and we landed with more than minimum reserves but it caused me to be really busy in IFR conditions.While direct to ZZZZZ1 to cross at 9;000; I was given an eastbound vector through the arrival track between ZZZZZ2 and ZZZZZ1 while descending at close to 3;000 FPM.  Then told to head direct to ZZZZZ1and cross it at or below 9;000.  This involved a 135 degree right turn within 10 miles of ZZZZZ1 but all was good on making the crossing altitude.  Then was given 5;000 at ZZZZZ and told to cross ZZZZZ1 at or below 9;000.  I entered the 5;000 in for ZZZZZ but made the error of entering a vertical 'Direct to' for ZZZZZ and engaging VNAV.  Looked up and the descent rate had switched from almost 3;000 FPM to just above 1;000 FPM.  Very quickly disengaged VNAV and dialed in the 3;000 FPM on the VS mode.Finally figured out there was no way I was going to make the crossing at ZZZZZ1.  Told the Controller I wasn't going to make the crossing altitude at ZZZZZ when within 2 miles of ZZZZZ1 - a little late.  We ended up crossing ZZZZZ at a little below 10;000 and the rest of flight went very well.Causes:  1st would be doing that VNAV to ZZZZZ - if I left everything alone; we would have been fine.2nd was coming in high and having to do a steep descent while being vectored around and given the direct-to really close to the ZZZZZ1 fix which involved lots of turning.3rd was flying a little slow and descending a little slow to save fuel which caused problems for ZZZ Approach.4th was getting barely any sleep the night before - had taken a natural energy booster later in the day and it didn't wear off until XAam or so then had to get up early.5th was keeping the flight smooth for the passenger despite the steep descent and all the turns - without a passenger I would have been more positive about getting down.6th was the low fuel situation I was concerned about - during COVID with lower air traffic I became used to getting unobstructed clearances but it is busy again - really busy this day and I didn't figure that I would have any problem getting a climb to 450; but I did and that burned more fuel than I had planned.How to avoid in the future:  1) Plan fuel for busier air traffic.  2) Don't do a VTO to the last of 2 fixes when given crossing restrictions for 2 fixes.  Either VS it or if using VNAV just do the VTO to the first fix and let the VNAV figure out how to get down to the second fix.  3) Don't take that energy booster after lunch time!  4)  I forgot that during descent the fuel gauges read a little low - just remember this next time.
Small Transport aircraft pilot reported not making a crossing restriction during approach due to numerous distractions.