An MP4 file is big when it has a high resolution, a high bitrate (data per second) or a long duration. You can lower the first two a lot before the difference is visible on a phone.

What makes the biggest difference

Resolution: 4K → 1080p cuts the size by roughly three quarters and still looks sharp on phones.
Bitrate: phone cameras record with a very high bitrate. A moderate bitrate keeps the look and saves a lot of space.
HEVC (H.265): saves space compared with H.264 at the same quality. Use H.264 if the video must play everywhere.
Frame rate: 60 fps → 30 fps for videos without fast motion.

Do it with Video Compressor & Resizer

Select the video and choose 1080p.
Pick a quality level, or a target size in MB.
Compress and compare the result with the original before deleting the original.

Do not compress twice: every compression loses detail. Always start from the original file.